Sewell’s Thermodynamic Failure


The young earth creationists (YECs) used to refer to the 2nd law of thermodynamics as an allegedly insurmountable obstacle to evolution. When their critics pointed out that the 2nd law, as used by creationists, is only valid for “closed” (or “isolated”) systems and therefore is not an obstacle to evolution on our planet which is an open system receiving energy input from the sun, the YECs suggested various specious arguments designed to circumvent this limitation of the 2nd law. With time, as straightforward young earth creationism gradually retreated to such fringe outlets as Answers in Genesis, the Institute of Creation Research, and Hovind’s entertainment shops (being replaced by intelligent design movement as the main anti-evolution force), reference to the 2nd law of thermodynamics has rare been heard as an anti-evolution argument.

However, this pseudo-scientific argument has not been completely abandoned by anti-evolution forces, both of YEC and ID varieties. From time to time it recrudesces in writing of this or that advocate of creationism.

One example of such a misuse of the 2nd law of thermodynamics is a recent article by professor of mathematics Granville Sewell titled “Evolution’s Thermodynamic Failure” (see here ).

When so great a “scientist” as Pat Buchanan endeavors to speak about evolution ( see here) there is little to be surprised about when he displays ignorance – Buchanan is a “pundit” of dubious integrity, with no credibility as far as any science is concerned, so we can’t expect from him a reasonable discourse about anything scientific. Likewise, when some of the fellows of the Discovery Institute assault evolution theory, distortions and misrepresentations are the order of the day, because that is how they earn their keep. However, when a professor of mathematics at a qualty university misuses thermodynamics, one only can shrug in astonishment.

Since I am not a mathematician, I would never try discussing the quality of Sewell’s mathematical publications. Perhaps he is a very good mathematician. That is not for me to judge. However, having taught all parts of physics, including thermodynamics, statistical physics, physical kinetics, and other related disciplines, for over half a century, both on the undergraduate and graduate levels, I feel qualified to judge Sewell’s thermodynamic exercise. I find it depressingly fallacious.

Let me quote certain passages in Sewell’s essay and briefly comment on them. Sewell starts his essay with the following words:

In the current debate over “Intelligent Design,” the strongest argument offered by opponents of design is this: we have scientific explanations for most everything else in Nature, what is special about evolution?

I don’t know where Sewell found the quoted statement: he provides no references. I can’t recall such statement offered as “the strongest argument… by opponents of design.” To me it looks more like a straw-man erected by Sewell to enable him easily defeat this allegedly “strongest” anti-design argument.

This telling start of Sewell’s thermodynamic exercise portends the overall level of his critique of evolution theory (ET). Indeed, as we read Sewell’s tract, what we see described under the label of evolution theory looks more like a caricature of that theory. Of course Sewell is not a biologist and is not expected to discuss evolution theory on a professional level, but if this is the case, would it not be more sensible to leave the discussion of the strong and weak features of ET to experts (as they have been doing day in and day out in thousands of papers in scientific journals and on conferences and meetings)? I guess that if some biologist not versed in mathematics endeavored to critique Sewell’s mathematical output, Professor Sewell would shrug off the dilettante’s exercise with a disdainful smirk.

Since I am not a biologist, I’ll limit my discussion of Sewell’s essay to narrow thermodynamic topics.

The main argument against the ET used by Sewell seems to be based on thermodynamics, and specifically on its famous 2nd law.

Before delving into the essence of Sewell’s main argument, let me provide a few more quotes from his essay.

Sewell writes,

The first formulations of the second law were all about heat:: a quantity called thermal “entropy” was defined to measure the randomness, or disorder, associated with a temperature distribution, and it was shown that in an isolated system this entropy always increases, or at least never decreases, as the temperature becomes more and more randomly (more uniformly) distributed.

First of all, this statement is historically wrong. When Clausius introduced the concept of entropy, it was not connected in any way with “randomness” – such a connection was discovered much later, and not in thermodynamics per se but rather in statistical physics. Furthermore, the expressions “temperature distribution” and “temperature becomes more and more randomly (more uniformly) distributed” are rather imprecise. Temperature T is a thermodynamic parameter which has meaning only for macroscopic assemblies of particles. T has no meaning for infinitesimally small volumes. We can meaningfully discuss temperature gradients, because the concept of a gradient does not require consideration of infinitesimally small volumes. However, the concept of a “distribution” involves the concept of a “distribution function,” which necessarily incorporates values defined for infinitesimal volumes where the concept of T is meaningless.

Sewell further writes,

The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room – unless this order is disappearing into our room, and then only if it is a type of order that makes the appearance of computers not extremely improbable, for example, computers. Importing thermal order will make the temperature distribution less random, and importing carbon order will make the carbon distribution less random, but neither makes the formation of computers more probable.

Note here the expressions like “order is disappearing in the next room,” “Importing thermal order,” and “will make the temperature distribution less random.”

While expressions like “entropy flows into the system,” are common in thermodynamics, they are just metaphors. Entropy is not a substance which can literally “flow” from or into a system. Entropy is a measure of disorder and the actual mechanism of its decrease in one place and accompanying increase in another place is statistical. It is realized via random motion of particles chaotically exchanging their energy and momenta through collisions. Likewise, expression like “order is imported,” have no literal meaning, but Sewell uses such expressions as if they reflect the actual influx (“import”) or outflow (“export”) of some non-existing substance called “order.” This metaphoric language sheds no additional light on the discussed phenomena, more so because his expressions like “temperature distribution becomes less random” are simply confusing as the temperature is essentially a macroscopic quantity having no meaning for infinitesimally small volumes and therefore a distribution function for temperature cannot be defined.

Defenders of Sewell may argue that I am nitpicking here on some insignificant semantic details. Perhaps this is so and these semantic details have no bearing on the essence of Sewell’s argument. They have a bearing, though, on the overall credibility of Sewell as the interpreter of subtle nuances of thermodynamics he evidently pretends to be.

Here is another quote:

Natural forces, such as corrosion, erosion, fire and explosions, do not create order, they destroy it.

Without a further “nitpicking” regarding the term “forces” being applied to corrosion and erosion (which are, strictly speaking, not forces but processes), Sewell’s thesis is contrary to well established facts which testify that there are many spontaneous natural processes that create order. Has Professor Sewell never heard about self organization which occurs spontaneously and has been observed many times in various systems? Has Sewell never heard about, say, Benard cells, a Belousov-Zhabotinsky reaction, spontaneous ordering in various colloidal systems, etc., etc., etc.? (See, for example, Niall Shanks, God, the Devil, and Darwin).

Regarding erosion, it certainly may cause destruction of information-rich structures. For example, erosion may result in a gradual deterioration of the Mount Rushmore carvings. However, in other cases erosion can create sculpture-like images. Has Professor Sewell never heard about erosion spontaneously creating amazing structures looking like animals, people, bridges, and the like? I’d recommend Professor Sewell travel to Russia and visit there the Dombai region in the North Caucasus. He may see there an amazing phenomenon – a mountain named Sulakhat – which looks like a sculpture by an accomplished artist in the shape of a young woman on her back, but is, in fact, an accidental grouping of rocks.

If the gradual destruction of, say, the Great Buddha sculpture is an example of the destructive force of erosion, which, according to Sewell, “destroys order,” then the appearance of sculpture-like images due to erosion, by the same logic, should be construed as creating order (of course this is, in fact, rather an example of creating the illusion of design). Here is how Sewell offers his main claim:

.… the idea that the four fundamental forces of physics alone could rearrange the fundamental particles of nature into spaceships, nuclear power plants, and computers, connected to laser printers, CRTs, keyboards and the Internet, appears to violate the second law of thermodynamics in a spectacular way.

Having announced the quoted claim, Sewell proceeds to elaborate, aiming to prove that the 2nd law of thermodynamics prohibits evolution.

I’ll concentrate now on Sewell’s thermodynamic argument.

Since Sewell’s argument is based on his interpretation of entropy and of the 2nd law of thermodynamics, perhaps it is proper to start with a brief discussion of what these concepts entail (see also my essay here ).

Sewell interprets entropy as a measure of disorder. In the context of this discussion, I readily accept such an interpretation. Here, though, my agreement with Sewell ends. IMO, the rest of his discourse abounds in faulty assertions, incorrect examples, and unsubstantiated conclusions.

As a preamble to the discussion of Sewell’s piece, let me conduct a brief excursion into the chapter of thermodynamics dealing with entropy and the 2nd law.

The concept of entropy was introduced by Clausius in a specific form as

Clausius noticed that while dQ is not a real differential but just an infinitesimal amount of “heat,” (because heat Q is not a function of state) the inverse temperature 1/T is what mathematically is referred to as integrating coefficient. Unlike dQ, the quantity dQ/T is a real differential. Integrating dQ/T produces a function S of the system’s thermodynamic parameters (such as pressure P, volume V, temperature T, magnetization B, etc.). This function (named “entropy” by Clausius) is a “function of state,” in many respect similar to temperature (with an important difference – T is an intensive, whereas S is an extensive property).

COMMENT. While entropy is legitimately construed as a thermodynamic parameter, or as a system’s “property” similar to the way volume, pressure, temperature, magnetization, etc., of a system are referred to as system’s “properties,” in fact entropy is not a physical property of system’s material constituents. For example, for a gas consisting of molecules, entropy is not a property of molecules, but a measure of disorder in the molecules’ distribution over locations in the volume they occupy, and/or of their momenta, etc. The term “property” is used in thermodynamics in a semantically different way than in, say, material science or physics of solids where the term “property” is reserved for ,say, mass, magnetization, polarization, strength ,elasticity, and other physical properties of a material, determined by its structure.

Clausius found that function S is an invariant of a reversible adiabatic process or of any reversible cycle (similarly T is an invariant of a reversible isothermal process or of any reversible cycle). Reviewing various processes and cycles, Clausius postulated that, in an irreversible process, the net entropy summed up for all participants of the process always increases. This postulate cannot be rigorously proven, but has been accepted, based on an extensive analysis of multiple situations, as the 2nd law of thermodynamics. (This law has many differing definitions discussed in textbooks on thermodynamics; however, for the purpose of this review adopting the above not quite rigorous definition is quite proper, because creationists usually base their thesis about the 2nd law allegedly prohibiting evolution, explicitly or implicitly, on a formulation dealing with the prohibition of entropy’s spontaneous decrease).

From the very beginning, it was realized that the postulate prohibiting a spontaneous decrease of entropy could not be substantiated for “open” systems. If a system has been chosen as such part of the universe whose boundaries allow for energy ingress or egress, then the entropy of such a system may change in various ways and its decrease is possible. The actual behavior of entropy in such an “open” systems is determined not by the prohibition of entropy decrease, but by local conditions, and is not limited to entropy increase (although the net entropy of the universe will only increase in every irreversible [i.e. in any real] process, regardless of which system it occurs in). Hence, even in its initial non-statistical rendition, the prohibition of entropy decrease was only formulated for closed (or isolated) systems, including the universe as a whole, or any part of it whose boundaries prohibit egress and/or ingress of energy and matter. Hence, alternatively, the 2nd law can be stated as “the net entropy of the universe necessarily increases in all irreversible processes.” In this formulation, the universe is considered a closed system (as there is nothing beyond the universe, no egress from or ingress to the universe of energy or matter can take place, which is what the concept of a closed system is all about). Since all real processes are irreversible, the 2nd law is a very general statement about the natural world.

It may be pointed out that Clausius’s formula for entropy is just a particular case since there are an infinite number of functions all suitable to serve as “entropy.” The sole requirement for a function to serve as “entropy” is its being an invariant of a reversible adiabatic process. Adiabatic process is such where there is no energy flow through the system’s boundaries. This is a limiting case wherein, unlike in any other processes, entropy remains constant. A reversible process is just an idealization as all real processes are irreversible, so the entropy of the universe necessarily increases in all natural processes, while the entropy of a part of the universe that is an “open” system may decrease as well, depending on the local conditions and the energy flow.

Moreover, the units (like Joule/Kelvin) of Clausius’s entropy are not inherent in this quantity. In theoretical physics, entropy is viewed as essentially a dimensionless quantity. (See, for example, L. Landau and E. Lifshits, Statistical Physics.)

A substantial impetus for a deeper interpretation of entropy was provided by the realization (by L. Boltzmann) that entropy is a monotonic function of the number of microscopic states accessible for the system. Boltzmann suggested a convenient logarithmic transformation from the “thermodynamic probability” W, which equals the number of accessible states, into Clausius’s entropy:

where k is the Boltzmann coefficient whose value was chosen to make Boltzmann’s statistically defined S coincide quantitatively with Clausius’s S.

Boltzmann’s work was instrumental in realizing the statistical nature of laws of thermodynamics (notably of the zeroth, the first, and the second laws). Laws of thermodynamics are not statements of absolute truth but just postulates, justified only in a statistical (probabilistic) sense. The predictions of the laws of thermodynamics are pointing to the most probable behavior of a system rather than to the 100% definite behavior. However, for sufficiently large system and for sufficiently long periods of time, the probability of a system behaving according to the laws of thermodynamics is so overwhelming that behavior contrary to the laws in question can usually be safely excluded.

The fact of the 2nd law (in its formulation prohibiting spontaneous entropy decrease) having a reasonable interpretation only for closed systems is profound. Indeed, what does the 2nd law say about open systems considered separately from the rest of the universe? Nothing in detail, except for stating that the reversible ingress of heat into it causes its entropy to increase while a reversible egress of heat causes entropy’s decrease. While asserting that in a closed system entropy cannot spontaneously decrease, the 2nd law cannot say anything like that about entropy’s behavior in open systems. As far as the 2nd law goes, in open system’s entropy can increase, decrease, or remain constant. Therefore any attempt to apply the 2nd law, in its formulation prohibiting entropy decrease, to open systems, is meaningless.

Entropy of an open system, whose boundaries allow for energy ingress or egress, can spontaneously decrease without contradicting the 2nd law. Contrary to Sewell’s thesis, there are many situations where entropy of an open system decreases spontaneously, and this in no way contradicts the 2nd law.

Does Professor Sewell not know, say, about the spontaneous solidification of melted metals? If a melt is cooling down, (as an open system does when the surrounding is cooler than the melt) at a certain temperature the disordered liquid spontaneously converts into crystalline structure of a solid, and its entropy spontaneously decreases. Sewell’s ruminations about “import of order” from the surrounding does not shed any additional light on this trivially known notion, as it is just Sewell’s peculiar way to assert the simple fact: while heat “flows” out of the system, the temperature and entropy of the sample drop, but the entropy of the surrounding, and with it of the entire universe, increases, thus satisfying the 2nd law (as the universe is considered a closed system).

Likewise, if a sample of a ferromagnetic material is heated up, at a temperature above its Curie point, it converts into paramagnetic state where the strong order in its spin structure disintegrates (and entropy increases, in agreement with the heat influx). However, if left intact in a cooler surrounding, the sample will spontaneously cool down (as per the 2nd law) and below its Curie point a strongly ordered spin structure will spontaneously set in, with a concomitant entropy decrease (and this is not at all contrary to the 2nd law). The above explanation leaves no place for any interpretation of the 2nd law of thermodynamics as allegedly prohibiting evolution: the 2nd law contains nothing justifying such a conclusion.

If Sewell’s conclusion about the 2nd law prohibiting evolution were true, life would be impossible. A living organism constantly (and successfully) fights against entropy increase. Were the organism a closed system, it would not be able to survive as all processes within the body would, as the 2nd law postulates, lead to the increase of entropy, and thus to the body’s rapid disintegration. Luckily, organisms are open systems and the 2nd law does not prohibit entropy decrease in such systems, hence not prohibiting increase of complexity or of informational contents of the system.

As a female becomes pregnant, a process starts wherein the entropy of the fetus, and with it of the entire female body gradually decreases and this is in no way contrary to the 2nd law because this law does not prohibit entropy decrease in open systems. The mass of the fetus increases along with its development, and entropy is an extensive quantity, this contributing to the increase of the total entropy of the “mother + fetus” system, but the differentiation of the fetus’s tissues is a domineering process resulting in a net decrease of entropy of said system (with a concomitant increase of the universe’s net entropy).

An animal’s body constantly exchanges energy and matter with its surrounding, so it is an open system for which entropy decrease is possible. Were Sewell right, such growth and development would be impossible, as would be the evolutionary process. The very existence of Sewell as a living person testifies against his anti-evolution pseudo-thermodynamic arguments. There is a case where the decrease of entropy is an observed fact. In this process another (non-thermodynamic) law is at work, ensuring entropy decrease. Such a law was suggested to be that of gravity (see, for example the online discussion of papers by Stewart and by Davies).

As living organisms constantly fight against their entropy’s increase, it is achieved at the cost of the overall increase of the universe’s entropy, thus meeting the requirements of the 2nd law. As the universe has been constantly expanding since the Planck time, the number of accessible states is increasing thus enabling the increase of the total entropy of the universe despite the existence of locations whose entropy decreases (caused, for example, by living organisms, or by gravity, which is one of those forces working against entropy increase).

The 2nd law has other limitations as well. For example, the 2nd law is not applicable to systems of small size, or for short periods of time. In a small system (say, consisting of only 100 particles) the probability of a non-uniform distribution of the particles is reasonably large, so a spontaneous increase of order is not as highly improbable as it is for large systems. This is better interpreted as considering entropy (like temperature) as an essentially macroscopic concept, having little meaning for small systems, and no meaning whatsoever for microscopic systems. This limitation may (or may not) be of consequence for the problem of abiogenesis, since the spontaneous generation of primitive original replicators might not have required the assembly of a large number of particles, so the 2nd law in such a case would not have imposed restrictions upon the outcome of the reactions.

Likewise, during short periods of time, fluctuations in the particles’distribution may result in a temporary increase of order. This does not contradict the 2nd law, which is true only statistically and is not applicable for short times or small systems.

Although the problems of abiogenesis (the origin of life) are beyond evolutionary biology, Sewell seems to conflate in his arguments two different problems – that of the evolution of the living organisms and that of the origin of life. In this vein, he repeatedly refers to laws of probability. Since Sewell is a mathematician, he is supposed to be versed in probabilities on a professional level. Unfortunately, his arguments based on probabilities are no better than similar arguments offered many times before by “creation scientists” of various kinds and shown many times over to be irrelevant to the question of origin of life. I have discussed this point at length before (see, for example, the chapter on probabilities in my book Unintelligent Design, or online see here ) so I’ll not repeat this discussion here.

Sewell further refers to Michael Behe’s notorious book Darwin’s Black Box and to the concept of Irreducible complexity (IC). He seems to have uncritically swallowed Behe’s argument, and shows no familiarity with the devastating critique of Behe by many mainstream scientists. Since I have made a modest contribution to the critique of Behe’s book (see, for example, chapter 2 in my book Unintelligent Design, or online here and here ) as well as in my article in Skeptical Inquirer, Nov-Dec 2005 issue, I see no need to repeat my anti-Behe notions here. The recent evisceration of Behe’s views by the plaintiff’s attorneys at Kitzmiller vs DASD trial (see here ) and in the Judge Jones’s decision (see here ) have vividly shown Behe’s inability to say anything of substance in defense of his IC concept.

Sewell further writes,

…there is no proof that natural selection has ever done anything more spectacular than cause bacteria to develop drug-resistant strains, where is the overwhelming evidence that justifies assigning to it an ability we do not attribute to any other natural force in the universe: the ability to create order out of disorder?

Doesn’t this passage remind one of an episode during the Kitzmiller trial? When Behe claimed the absence of any scientific data about the emergence of IC systems, the plaintiff’s attorneys placed upon a table a pile of 58 peer-reviewed papers and 9 books doing exactly what Behe claimed to have never been done. While Behe, in his amusing self-assurance, might not have realized it, the judge and every unbiased observers construed this episode as a milestone on the way to completely discrediting Behe.

Likewise, claiming the absence of “proofs” for ET, Sewell just reveals his lack of familiarity with the pertinent literature. The fact of speciation (often referred to by creationists as “macroevolution”) has been firmly established by observation and experimentation (see, for example Jerry Coyne and Alan Orr’s book Speciation or online for example, here or here .

I believe the above quotations are sufficient to see Sewell’s essay for what it is – a groundless diatribe which could be expected from a semi-literate emotional anti– evolutionist, but sounds preposterous coming from a professor of mathematics.

(A general remark: evolution theory cannot be proven or rejected by applying any mathematical equations or laws of physics. ET is an empirical science based on immense experimental and observational material. The fact of evolution has been established beyond a reasonable doubt, although mechanisms of evolution continue to be discussed by evolutionary biologists. If certain mathematical equations or laws of physics seem to contradict ET, the reasonable explanation is that the equations or laws in question have been misapplied or misinterpreted.)

Sewell’s essay ends with the following sentences:

The development of life may have only violated one law of science, but that was the one Sir Arthur Eddington called the “supreme” law of Nature, and it has violated that in a most spectacular way. At least that is my opinion, but perhaps I am wrong. Perhaps it only seems extremely improbable, but really isn’t, that, under the right conditions, the influx of stellar energy into a planet could cause atoms to rearrange themselves into nuclear power plants and spaceships and computers. But one would think that at least this would be considered an open question, and those who argue that it really is extremely improbable, and thus contrary to the basic principle underlying the second law, would be given a measure of respect, and taken seriously by their colleagues, but we aren’t.

In fact, the 2nd law of thermodynamics is not really “the supreme law of Nature,” although it is one of the widely applicable and highly plausible postulates of science. However, anti-evolutionists often exaggerate its significance and applicability. A common thesis of anti-evolutionists has been the assertion that according to the 2nd law “everything” in nature tends to decay, degenerate, and lose its ability to be used. They often offer examples such as talking about a glass that fell on the ground and broke, which will never spontaneously recombine into a whole glass. While this statement is correct in itself, it in fact has little to do with the 2nd law of thermodynamics (as should be clear from the explanation of that law given above). Likewise, the assertion by anti-evolutionists that “everything” in nature tends to decay, etc, is an exaggeration. Recall the adage “diamonds are forever.” Items made of gold, platinum, iridium, rhenium, molybdenum, tungsten, stainless steel, and many other materials may remain intact indefinitely. Some metals (liked gold) are corrosion-resistant simply because of their electrochemical properties. Some other resist corrosion because on their surface spontaneously appears a thin but very strong layer of oxides, protecting the item from corrosion. If this layer is mechanically removed, say by filing the surface, it immediately spontaneously reappears. A gold item, if left alone, can remain intact indefinitely long, regardless of the 2nd law of thermodynamics. The same is true for many other materials, such as various semiconductors, dielectrics, etc. The assertion about “everything” necessarily decaying is an exaggeration, often used by creationists to “prove” that the 2nd law makes evolution impossible.

I wish to point now to the concluding sentence in Sewell’s essay, where he complains that anti-evolutionists are not “taken seriously by their colleagues,” and are not “given a measure of respect.”

I’d like to ask Professor Sewell whether or not he agrees that when “respect” is requested, it should be a two-way street?

In an essay I wrote with Wesley Elsberry (see here) we documented multiple examples of ID advocates using insidious comparisons of their adversaries with the Nazis, Soviet communists, Salem judges, the Taliban, Lysenko and other similar personalities and regimes.

After I published my book Unintelligent Design and posted a number of anti-ID and anti-creationism essays on the internet, I was honored by pro-ID and pro-creationism advocates with such signs of respect as publicly calling me in their posts stupid, moron, pest, liar, hypocrite, “close,” and other similar nice appellations. I was accused on pro-ID sites of lying about my list of publications and patents. I was accused of not being able to comprehend simple mathematics, of not comprehending “plain English,” of deliberately trying to misrepresent ID, etc., etc., etc. Other critics of creationism often get a similar treatment from advocates of both ID and YEC. The “great philosopher” of ID William Dembski, who never published a single word in response to the essence of my critique of ID, called me, apparently trying to be witty, “Boris Yeltsin of higher learning.” While the meaning of that appellation remains Dembski’s secret, nobody would interpret it as a manifestation of respect and of a serious attitude to my work.. Professor Sewell, when requesting respect, please don’t forget the saying “Doctor, heal yourself.”

My thanks to Nick Matzke for pointing to Sewell’s essay, and to Marshall Berman, Andrea Bottaro, Glenn Branch, Pete Dunkelberg, Gordon Elliott, Wesley Elsberry, Erik, Paul Gross, Art Hunt, Mark Isaak, M. Kim Johnson, Steve Reuland, Jason Rosenhouse, Douglas Theobald, and the entire PT team for pithy comments.


Excellent post.

If Professor Sewell is so confident that the 2nd law of thermodynamics disproves evolution, why hasn’t he tried to publish in a peer-reviewed journal? It’s telling when someone sneaks an essay about evolution into the appendix of a math text book.

Were Sewell right, such growth and development would be impossible, as would be the evolutionary process. The very existence of Sewell as a living person testifies against his anti-evolution pseudo-thermodynamic arguments.

Exactly. If entropy works the way creationists describe, mere growth would be impossible as well.

After readers finish checking their “carbon order” pace Sewell to be sure they aren’t disintegrating, they can gain some insight into Prof. Granville Sewell from his articles on his son Christopher’s site.

Excellent article! This is exactly the reason Panda’s Thumb is such a stellar resource.

Excellent article, but 99.9% of Granville’s readers will skip right over it. Too long and too much information. (And no pictures!) We need to make it much, much shorter. My suggestion:

The sun converts hydrogen into helium, giving off enormous amounts of radiant energy in the process, and this increases the sun’s entropy.

Living things on the earth use the sun’s energy to convert raw materials into more organisms, lowering the earth’s entropy in the process.

One particular form of earthly life is called “human” and female humans use the sun’s energy to create new humans in their womb.

Those humans will then use the sun’s energy to “rearrange the fundamental particles of nature into spaceships, nuclear power plants, and computers, connected to laser printers, CRTs, keyboards and the Internet, [which] appears to violate the second law of thermodynamics in a spectacular way [if you don’t know jack about physics].”

If it’s your magazine’s policy to have intelligent men write foolish articles about fields they are ignorant of, making your magazine look like a convention of cranks in the process, then I suggest you solicit further articles from the creationist/ID movement. They won’t fail you.

A small suggestion. Whenever entropy decreases in an open system, the decrease is more than matched by a consequent increase in the entropy of the universe at large. For example, crystallization releases heat; gravitational collapse releases heat; metabolism releases heat.

This is a consequence of allying the three laws of thermodynamics. 1) (matter-)energy cannot be created or destroyed. 2) the entropy thing and 3) 100% conversion of energy to work is impossible.

here’s my argument using the analogy that d(entropy)/dt = “flow”

a living system accelerates the flow of entropy and harvests a small portion of the difference between the normal and accelerated flow rates to generate WORK, which is used to build a local (and transient) increase in order.

the consequence of the third law is that this conversion is inefficient an therefore that overall, the presence of life causes things (“the universe”?) around it to break down FASTER than they would in the absence of life. in fact, life accelerates decay and is therefore completely compatible with the second law, even on this ‘universal’ level.

But the universe as a whole IS a closed system, is it not? Thus the expectation, based on the second law, is that its entropy will continue to increase. So the earlier in time we look, the entropy of the universe should be decreasing, to ever smaller and smaller values. This cannot go on forever, since entropy cannot be negative, by definition. All this leads to some very interesting and troublesome problems for cosmology, particularly if one is an atheist.

Superb piece. I’d seen the original Sewell article and I was waiting for someone with better knowledge of physics than my own to do a detailed rebuttal.

On the point that the piece is too long and complicated I would suggest wrapping it up in the pithy one liner:

“The very existence of Sewell as a living person testifies against his anti-evolution pseudo-thermodynamic arguments.”

But the universe as a whole IS a closed system, is it not? Thus the expectation, based on the second law, is that its entropy will continue to increase. So the earlier in time we look, the entropy of the universe should be decreasing, to ever smaller and smaller values. This cannot go on forever, since entropy cannot be negative, by definition. All this leads to some very interesting and troublesome problems for cosmology, particularly if one is an atheist.

Who suggests this will go on forever? Why would this bother atheists?

Carol writes “But the universe as a whole IS a closed system, is it not? Thus the expectation, based on the second law, is that its entropy will continue to increase. So the earlier in time we look, the entropy of the universe should be decreasing, to ever smaller and smaller values. This cannot go on forever, since entropy cannot be negative, by definition. All this leads to some very interesting and troublesome problems for cosmology, particularly if one is an atheist.”

Does the word “asymptotic” mean anything to you?

Where in blazes to you get the idea that as one goes back in time entropy of the Universe can’t approach a finite, positive value?

But the universe as a whole IS a closed system, is it not? Thus the expectation, based on the second law, is that its entropy will continue to increase. So the earlier in time we look, the entropy of the universe should be decreasing, to ever smaller and smaller values. This cannot go on forever, since entropy cannot be negative, by definition. All this leads to some very interesting and troublesome problems for cosmology, particularly if one is an atheist.

I guess we could simply redefine the Universe as something that is not required to obey the 2nd law of thermodynamics instead? No? Then why should God be exempt? Because the Bible says so? As a Christian you have some very interesting and troublesome problems to consider…

I guess we could simply redefine the Universe as something that is not required to obey the 2nd law of thermodynamics instead? No? Then why should God be exempt? Because the Bible says so? As a Christian you have some very interesting and troublesome problems to consider…

All signs point to that the universe as we know it will end one day. So what? How is this proof for god?

BTW, I heard that Carol is a jew…

God is exempted because god is God is GOD is G-O-D.

Eugene et alii: i think you misunderstood the direction of Carol‘s arrow.

What’s the problem? All she’s saying is that at the beginning of the Universe, entropy was essentially 0 (i.e. that the Universe was nearly perfectly ordered).

This makes perfect sense to me, since everything that was to become the Universe was packed into a mind-bendingly small volume (by my extremely limited understanding of string theory [only by reading Brian Green’s “The Elegant Universe” twice– I’m a biologist, not a cosmologist!!], no dimension can be smaller than the Planck length [1.6 x 10^-35 m]). Near Perfect order = near 0 entropy!

Personally, I don’t see any problem with this nor how it has any relationship to (a)theism at all.

djmullen Wrote:

The sun converts hydrogen into helium, giving off enormous amounts of radiant energy in the process, and this increases the sun’s entropy.

This is a common error. The Sun is actually an example of a local decrease in entropy; a common phenomenon in the natural world and a further demonstration of the ignorance involved in creationist invocations of thermodynamics.

The common claim made in response to creationists is that any local decrease of entropy on Earth is compensated by a greater increase in entropy in the Sun. This is wrong.

So where is the entropy increase to satisfy the second law? It is in the vast cold reaches of empty space, which is receiving hot radiation from the Sun. There is a continuous flow of energy from the Sun (a hot object) into empty space (a cold reservoir). So it is empty space that increases in entropy as the Sun decreases in entropy. The Earth taps into this energy flow, receiving hot radiation from the Sun, and then re-radiating this into empty space as infra-red radiation (much cooler). The radiation in balances the radiation out, but the radiation in carries less entropy.

Here are some sample calculations. Consider 1000 J of thermal energy from the Sun. The Sun’s surface is about 5700 K; and the Earth’s surface is about 290 K. The Sun decreases in entropy by 1000/5700, which is about 0.175 J/K. The Earth increases in entropy by 1000/290, which is about 3.45 J/K. So this energy from the Sun actually involves the Earth increasing in entropy. Of course, this cannot be the end of the story. The Earth is an open system, and it radiates back out into space. That 1000 J increase in thermal energy will eventually radiate back out into space, which has a temperature of about 2.7K; this 1000/2.7, or about 370 J/K entropy increase in the universe outside the solar system.

It is the capacity of Earth to taken in hot energy, and then dump it into cool space that allows local thermodynamic systems to do useful work on Earth.

I thought Carol is projecting into future; Having read djlactin post I now realise she is really projecting into the past.

In that case, I would think two word “Big Bang” would suffice.

The rest of my response remains intact: So what? How is this proof for god?

God is exempted because god is God is GOD is G-O-D.

... Wrote:

Excellent article, but 99.9% of Granville’s readers will skip right over it. Too long and too much information. (And no pictures!) We need to make it much, much shorter. My suggestion:

The sun converts hydrogen into helium, giving off enormous amounts of radiant energy in the process, and this increases the sun’s entropy.

The problem with this description is that it is just plain wrong. There are two errors:

First (minor): Stellar fusion is not increasing entropy. Fusion of four particles (hydrogen) into only one (helium) that remains in the sun actually decreases entropy for statistical reasons.

Of course the additional escaping photons and neutrinos are increasing the entropy of the surrounding universe.

Second (major): Giving off enormous amounts of radiant heat is not increasing but decreasing the entropy of an open System. Remember, the change of entropy is dS=dQ/T. Giving away heat is a negative change of heat, so dQ is negative. Since T is positive dS will be negative, too.

Again you will find the increase of entropy in the surrounding universe: For example if the sun gives away 1000J at a temperature of 6000K the suns giveoff of entropy would be 0.17J/K. The surrounding universe gets the same amount of energy, but since its temperature is only 3K its entropy will increase by 330J/K.

Mark Perakh Wrote:

An animal’s body constantly exchanges energy and matter with its surrounding, so it is an open system for which entropy decrease is possible. Were Sewell right, such growth and development would be impossible, as would be the evolutionary process. The very existence of Sewell as a living person testifies against his anti-evolution pseudo-thermodynamic arguments.

…a succinct summary of the whole piece! Isn´t the “SLOT” argument discredited even in creationist circles, nowadays?

Of course the very existence of Sewell as a living person might be a heavenly miracle.

But what if I, as an atheist, am assembling a computer? Am I doing a heavenly miracle then, too?

If I can do heavenly miracles, could not the evolutionary process like science is describing it happen as a heavenly miracle, too?

But of course if this kind of heavenly miracle is so common it might be more convinient to simply describe it as the way nature works according to its laws.

Items made of gold, platinum, iridium, rhenium, molybdenum, tungsten, stainless steel, and many other materials remain intact indefinitely.

Not completely true. On a timescale much larger than the lifetime of the sun, they are not. Furthermore stainless steel is a composite material and perhaps not the best example to give? For example, it does rust.

Posted by Chris Ho-Stuart on January 3, 2006 05:19 AM (e) (s)

djmullen wrote: The sun converts hydrogen into helium, giving off enormous amounts of radiant energy in the process, and this increases the sun’s entropy.

This is a common error. The Sun is actually an example of a local decrease in entropy; a common phenomenon in the natural world and a further demonstration of the ignorance involved in creationist invocations of thermodynamics.

djmullen: Hey, great! They can hire me! Anybody know how much they pay?

I’m no scientist but whenever I see this particular argument, I wonder why no one talks about Gibbs free energy. IIRC a reaction can be spontaneous and have a reduction of entropy as long as the reaction is sufficiently exothermic.

Hey Carol, why do you think science shoudl consider your religious opinions as “evidence”?


as long as the reaction is sufficiently exothermic

means that for such a reaction to proceed spontaneously, the entropy increase in the surroundings must exceed the entropy decrease of the reaction system. no violation there.


The point is that if as we go back in time the entropy of the universe (a closed system) MUST continue to decrease (in the context of the second law), and entropy cannot be less than zero, then we are in tight corner. Either the law is violated or the universe had a true beginning. Either scenario is fertile territory for creation by God.

Now, how does God relate to entropy? Well, since entropy is related to the number of states in phase space available for a macroscopic system of particles, and God is not particulate, the law and the concept of entropy do not apply. This is somewhat akin to Mark’s comment above that the law is not applicvable to systems of a small number of particles.

Carol, if he is not particulate, is he then perhaps a wave? Or, if we go small enough (as you imply), he can be both, but then we won’t know where he is. Hey, we don’t, so perhaps he is a photon. This would explain being many places at once? On the other hand, he would not exist, until he is observed now, would he? Have you observed him? If not, then let’s keep this discussion towards the things we do observe. That’s what science is all about, remember?

Granville Sewell appears to be a rather poor Christian.

Christianity teaches humility and honesty.

Sewell makes arrogant commentary on a subject of which he is ignorant. Clearly, he pridefully assumes that his expertise in mathematics somehow confers a near-psychic ability to be an expert in other fields, without taking the time to learn anything about them.

His verbose and pompous writing style is indicative of an ego bursting with arrogant hubris.

While his statements are more deluded than dishonest, they are to some degree dishonest as well.

An experienced academic, he could have easily checked the facts before publishing.

He bandies his expertise in one field to trick the innocent reader into mistakenly assigning him expertise in another field altogether.

I don’t know much about American Spectator. I do know that they, and Professor Sewell, have profoundly embarrassed themselves with this nonsense.

Carol you are loosing energy WWWWWHHHHHHHhhhhhyyyyyy.….? Wow g-d did what ?

Oh you provide evidence… of course… now I see it with my own eyes You better get that off to the Nobel Committee before Blast or Huddle sees it :)

So just how did the the macroscopic particle dictate the Grand Old Program to those really nice people that decided to take a LOOOONG holiday from Pyramid Building ? Or even smuggle in all those verses into the ghetto in Babylon where the conquers of the day decided to “relocate” the chosen people instead of the normal practice of the day …killing them all … Or where does Cyrus the Great the Persian empire builder who allowed each belief system to flourish through local Kings and he was given the Gentile title “The King of Kings” who restored the chosen Babylonian exiles to home and encouraged them to build their temples since after all THEIR GOD had decided that in a multicultural Kingdom it would be much better to have a reality system that moved the g-d thingy idea further out into the universe and jazzed things up a bit so good and evil were decided on a day of judgment at the end of the world instead of at the end of a battle which previously had the nasty habit of denuding the landscape of useful slaves.. when a messiah thingy would come on down them ol steps to heaven to reward them all for being good and not wiping out their neighbors.

Much easier to rule competing races when you’ve figured that one out! Then I digress. Where were we?.…oh yeah…creating reality. Magic thing reality…especially when you want to rule the world.

I am reminded of an article that came up on Google News this morning. It begins thusly:

The start of a new year is always full of some amount of trepidation about what unknown tangents the future will bring. Then a rapper gets shot and you realise that this year will be just the same.

And here we see that people are still trying to argue against evolution via the second law of thermodynamics, and Carol is still holed up in the twin alamos of First Cause and quantum mechanics with her vanishing God.

Same s***, new number.

I was going to take a shot at rebutting Sewell’s essay, but Mark’s done such a complete job, I’m not going to even try.

I have one general comment about entropy and evolution, though. The idea that as organisms evolve, their entropy somehow decreases, seems to be a product of sloppy and perhaps religious thought, and has very little scientific validity. We don’t know what the entropy of a ‘typical’ 100 g organism in the Cambrian was, compared with a 100 g mammal today, but there is absolutely no reason to believe it was higher; in fact, since the mammal is likely to be warmer, all other things being equal, the Cambrian animal is likely to have a lower entropy. A 200 lb human probably has about the same entropy as a 200 lb calf, and likely has a higher entropy than a 200 lb alligator (except on a very warm day).

The configurational entropy of the human genome is minuscule, and if I had to define it, I would have to count the number of possible DNA base permutations of the human genome (easy) vs. all the permutations that leave a human essentially unchanged (hard). But even comparing the genome of a human with the conjectured genome of a reptilian ancestor, it’s not at all clear the configurational entropy of our genome is lower.

Even if you compare the entropy of a 200 lb human with the entropy of 200 lbs of rock, we don’t win on the ‘more ordered’ sweepstakes.

Carol, if he is not particulate, is he then perhaps a wave? Or, if we go small enough (as you imply), he can be both, but then we won’t know where he is.

Perhaps he’s a piece of string.


Andrew McClure Wrote:

Wikipedia (yes, I know, not the best source, but I don’t have a better one at hand) gives two definitions of “entropy”. The thermodynamic definition of entropy, introduced by Rudolf Clausius, where change in entropy is equal to change in heat divided by absolute temperature; and statistical entropy, introduced by Boltzmann, where entropy is an absolute value, equal to a constant times the natural logarithm of “the number of possible states in the system”.

By the Clausius definition above, on the face of it I see no good reason why any particular entropy value could be described in non-relative terms. No absolute markers are defined or even really important, as far as I can see; we’ve got a differential, and that’s all we have to work with. By the Boltzmann definition however entropy itself is defined as a discrete quantity, and “zero” is obviously both meaningful and an absolute lower bound, since there will always be at least 1 possible state.

Are these two definitions of entropy the same, or not? Because if the two definitions are describing the same “entropy”, that seems to say to me that entropy has an absolute zero-like lower bound even if we are working with the differential, thermodynamic definition (even if we can’t experimentally measure that absolute value, it’s still there). What is going on here?

The Boltzmann (statistical) definition has been highly successful in understanding entropy, at least in terms of chemistry. As someone noted before, entropies of substances are now calculated to a high degree of certainty using statistical methods.

To answer your question, statistical mechanics shows that the Boltzmann definition of entropy yields the Clausius definition if applied to a large number of particles. That is, they are both consistent.

The 3rd Law of Thermodynamics posits that the minimum value of entropy possible is zero, and that can only occur at zero Kelvin. The 3rd Law is, like any other “law” of science, a statement of behavior supported by tremendous evidence. There is indeed ample evidence that the entropies of many substances approach zero as the temperature approaches zero Kelvin. It is the basis of the “absolute” entropies. In fact, absolute entropies are also called 3rd Law entropies because they start with the fact that entropy is zero at zero Kelvin.

For calculating entropy, enthalpy, or Gibbs energy changes in atmospheric processes, you could use either entropy definition (Boltzmann or Clausius). For your purpsoses, knowing the change in these quantities was probably sufficient, so you could use the Clausius definition.

Because the Boltzmann definition relates to the microscopic level and what’s going on at the scale of the atom, it is probably viewed as the more powerful definition.

OK, thanks.

Gerard Harbison Wrote:

Far too many people on this thread are dishing out complete twaddle with complete assurance.

That’s true. I’m not sure if you’re lumping me in with that group, but I left out residual entropy because it doesn’t add anything to the discussion (such as it is).

laser Wrote:

I’m not sure if you’re lumping me in with that group,

Not at all.

Far too many people on this thread are dishing out complete twaddle with complete assurance.

I, on the other hand, am dishing out complete twaddle with no assurance whatsoever.

So you’re saying I can know the “absolute entropy”, let’s say, of a gram of sugar - not just the changes relative to the corresponding elements.

What is it? (or, more seriously, how do I calculate it?)


As some other very recent posters have correctly pointed out, entropy is an absolute quantity with zero as a lower bound. The differential equations involving the quantity S are, of course, correct, but are not the defining statements for entropy as we see it these days. Would you not think it a bit strange and convoluted that a quantity would be defined solely by making statements about changes in the quantity?

Also, there are laws and there are laws. The word is frequently misapplied, just as theory and hypothesis are. There never really was a law against spontaneous generation, no matter what the typical biology text says. Just a statement that it (spontaneous generation) is highly unlikely to occur (yet again) under the changed conditions on earth (now teeming with life), so that if you see life anywhere the odds are overwhelming that it descended from other life.

Another example of a phony “law” that comes to mind includes “bode’s law”.

But the SLOT, like the laws of motion and gravity are serious laws. We do expect them to hold and would be amazed if they were ever found to be violated. This is why the courts routinely reject patent applications that are deemed to violate the SLOT (known as perpetual motion machines).

Syntax Error: not well-formed (invalid token) at line 8, column 269, byte 735 at /usr/local/lib/perl5/site_perl/mach/5.18/XML/ line 187.

Carol Landa Wrote:

Would you not think it a bit strange and convoluted that a quantity would be defined solely by making statements about changes in the quantity?

No, I wouldn’t. In fact, I work with such a quantity daily as an electrical engineer. It’s known as electrical potential, or more commonly, voltage. All voltages are referenced to an arbitrary potential (often called ground). There is no absolute ground.

There has been a good deal of confusion in this thread concerning the Third Law of Thermodynamics - which is not a surprise, since there is a good deal of confusion about it in the textbooks, even in some of the better ones. The best discussion I know of is in “Statistical Physics”, by Gregory Wannier. (Wannier was an exceptionally careful thinker.)

Lars is correct - the Third Law does not require us to set the entropy equal to zero at T=0. It merely permits us to do so. The physical content of the Third Law is that as T ->0, the entropy change associated with any process - any transformation of the system into another system - vanishes. This allows us to say that all systems have the same entropy at zero temperature. Also, every system has a higher entropy at any nonzero temperature than it has at zero temperature (this follows from the fact that the heat capacity Cv is positive, which is required by certain thermodynamic stability criteria). So by convention we set the “universal floor value of the entropy” equal to zero.

David Heddle has misunderstood Fermi - note that on the same page from which David quotes, Fermi correctly states the Third Law as:

“The entropy of every system at absolute zero can always be taken equal to zero” and follows up with “It is obviously convenient to choose one of the states of the system at T=0 as the standard state O introduced in section 12.”

As for Boltzmann’s formula S = k Log W, as presently interpreted it does incorporate the convention S(T=0) = 0. However, in Boltzmann’s interpretation it did not do so (note that Boltzmann’s equation preceded the Third Law by quite a few years.) This is because Boltzmann’s formulation was based on classical statistical mechanics, in which the “state” of a system is a continuous quantity. The “number of arrangements” or “number of complexions” of a classical system is not absolute (since the states can be arbitrarily finely grained), it is a relative quantity. A change in the scale of measuring coordinates and momenta produces a multiplicative factor in W, which results in an additive constant in S. I doubt that the idea of entropy as an absolute quantity ever entered Boltzmann’s head. However, when we carry Boltzmann’s formula over to quantum statistical mechanics, W does become an absolute quantity since the states are now a discrete set (I’m assuming that the system is confined to a finite volume so that the spectrum is discrete.)

As someone has pointed out upthread, it’s not really a good idea to talk about the “entropy of the universe” in any literal sense because on cosmic scales the laws of thermodynamics have to be modified to take into account general relativity. But it’s perfectly reasonable as a shorthand way of saying, “in any spontaneous process, the entropy of the system together that of its surroundings must increase” - just take care that the scale of the system and any surroundings with which it interacts is small compared to, say, a galaxy.

Finally, a minor technical quibble wrt Mark’s excellent post: the entropy is not in general given by dS = dq/T but rather by dS = dqrev/T, where dqrev is the heat flow in a hypothetical reversible process. In any real process, dS is greater than dq/T. (No doubt Mark left this out for brevity as it plays no role in his argument, but I didn’t want someone else to get confused - I’ve seen a lot of students come to grief over this point, as confusing dq with dq_rev can cause no end of trouble in solving problems.) This leads to a very pretty and very useful statement of the Second Law that is correct for open systems as well as closed ones:

For any spontaneous process, dS >= dq/T

where dq is the heat flow across the boundary of the system. If the system is closed, dq = 0 and you get back the law of increase of entropy. If the system is open, you can use the formula to calculate how much heat has to flow out of the system in order for the entropy of the system to decrease. By combining this inequality with the First Law (dq + dw = dE), you can easily derive the usual expressions involving Helmholtz or Gibbs Free Energy in the special cases of constant volume or constant pressure systems.

You can conclude immediately, for example, that in an endothermic reaction the entropy of the system must increase, but in an exothermic reaction it can decrease (and you can calculate just how exothermic it has to be.) Of course, you can do all of this by assuming that the system and its surroundings form an overall system that is closed, and then require that the overall entropy change of the composite system be positive - in fact, this amounts to doing the exact same mathematics with different words attached to the equations - but I find it useful to emphasize that you do not actually have to use this sort of language, you can instead focus on the system itself. The laws of physics are usually easiest to apply when formulated locally, and thermodynamics is no exception.

Robert Parson has misunderstood Fermi. He has read only the first page or so of the chapter, where after making the crystal clear statement that I quoted:

We have already found, however, that cases arise (for example in dealing with gaseous equilibria, Chapter VI) for which the knowledge of this constant becomes important. In this chapter we shall introduce and discuss a principle that will enable us to determine the additive constant appearing in the definition of entropy.

Fermi then has a brief classical discussion–at which time he makes the statements Parson quoted–but then goes on to a QM discussion where he shows that the Entropy constant can be determined (not chosen) just like he promised in his intro.

Fermi writes (p. 141)

The arbitrariness associated with pi (#microstates–Fermi uses the term dynamical states), and therefore the entropy also can be removed by making use of the principles of the quantum theory

By limiting the edge of phase space cells to Plank’s constant–in effect the theory is regularized and the arbitrainess is gone. Fermi writes (p. 142):

all indeterminacy in the definition of pi, and therefore in the definition of the entropy also, disappears.

Carol Clouser wrote:

Some smart guy asked “Who designed the designer?” Well, the point is that the logic of the situation dictates the existence of an entity that has no features, no particular parameters and therefore no design.

Carol you seem to be rather enamored of logic. Can I take it to be that you really seem to think that logic is important? That it should be taken seriously by one and all?

Carol further wrote:

The difference is, one exists and can act,

That is an assertion. Evidence?

I have another question, but it can wait.

Sincerely, Paul

David Heddle is confusing thermodynamics with statistical mechanics. The entropy of statistical mechanics is conceptually a very different thing from the entropy of thermodynamics, although it becomes numerically equal to it in the limit of a large system.

The Third Law of Thermodynamics implies that all systems at equilibrium have the same entropy at the absolute zero of temperature. It does not prescribe a value for this zero-point entropy - it cannot, since no measurable quantity depends upon this choice.

The statistical mechanical definition of entropy has several conventional features - the base of the logarithm, the proportionality constant, and an additive constant. These are all chosen so as to make the connection to thermodynamics as simple as possible. There is nothing to prevent us from writing S = k Ln W + 2.7 - that would correspond to a thermodynamic entropy in which the universal lower bound was 2.7 instead of zero. Just as there is nothing to prevent us from choosing a different value for k, or a different base for the Log - that would simply correspond to measuring entropy in different units.

Having taught both level thermo and stat mech at the grad level I think I know the difference. If you want to insist that (since I am using his book as a source) Fermi’s definitive statements are really meaningless, that when he writes “all indeterminacy in the definition of pi, and therefore in the definition of the entropy also, disappears” he really means “except for the arbitary additive constant which we knew about before this chapter but in spite of the stated purpose of this chapter is still in place (which renders this chapter meaningless)” then go right ahead.

The discussion in this thread was along the lines “entropy is relative, only differences matter.” That is certainly true in most calculations–however a QM treatment demonstrates that it is not strictly true.

Almost everything in stat-mech, not just the entropy, is (or can be) conceptually different. Not just the entopy. Nevertheless, pressure in stat-mech is the same pressure we talk about in thermo (although conceptualized differently), and entropy is the same entropy.

Carol, I’m still waiting for you to tell us why Heddle is wrong about the New Testament.

Heddle, I’m still waiting for you to tell us why Carol is wrong about the New Testament.

And I’m still waiting for either of you to explain why science should give a flying fig either way.

In two days since I posted the review of Sewell, close to 200 comments appeared in this thread. I think such a large number of comments makes the thread unwieldy. Moreover, while some comments were relevant and insightful, a substantial fraction of comments deviated from the topic, and, unfortunately, some commenters chose to be rude, insulting, and arrogant. I shall not name these people, who seem to be so sure of possessing the ultimate truth that they feel entitled to pounce on those who disagree with them by calling names and denigrating their opponents. I feel uncomfortable seeing such a behavior regardless of whether or not the offenders share or reject my position. In view of the above, I shall, after having posted this message, close comments for this thread.

Before doing so, I’d like to thank all those commenters who submitted messages of substance, regardless of whether I agree with their arguments. Of course, I especially appreciate those comments where their authors commended my essay, but I also value comments critical of it.

A few words about the debate regarding entropy, the 3rd law of thermodynamics, and other similar points. I wondered why some of these points invoked such a debate — they are in fact uncontroversial and commonly accepted in physics. For example, as Robert Parson correctly wrote, it is a commonly accepted view in physics that in classical statistics entropy has no definite value (while its behavior is determined by Nernst theorem stating that as the temperature of a system approaches absolute zero, its entropy approaches a certain value which, however, includes an arbitrary constant). On the other hand, in quantum statistics, as a system approaches absolute zero, its entropy approaches zero. There is no debate about it.

Some commenter wrote that he could meaningfully define temperature of a single molecule. I’d be surprised if he indeed could do so. I expect that, whatever his definition of such T will be, it certainly will be not the same T as the conventional thermodynamic temperature is.

Some commenters pointed to my passage about corrosion resistance of noble metals. I must concede that this particular passage in my text was sloppily formulated and there is nobody to blame but myself. I did not mean to say that gold’s corrosion resistance is due to an oxide layer (as is the case with some other metals) but when I re-read the pertinent paragraph in my text, I saw that it certainly created an impression that the point about passive film could be understood as related to gold. I have made a necessary editing in that paragraph - the corrected version is available at TalkReason website see here and I will make a similar correction in the post here shortly.

Robert was also right to point out that when discussing the universe as a whole, classical thermodynamics is inadequate and cosmology has to be delved into, accounting for the general relativity. Related to this point, there was a debate here about the value of the entropy of the universe at the initial moment of its existence. I believe there is no commonly accepted view on that point, although the prevalent interpretation seems to be as follows: nothing can be said about the universe before the Planck time. At the Planck time the universe is believed to have been fully disordered so its entropy had maximum possible value for the situation in point. As the universe has been continually expanding after the Planck time, its expansion has been continually creating more and more accessible states, thus opening ways for entropy increase, according to the 2nd law, above its value at the Planck time. Gravity caused local entropy decrease, as clusters of matter coalesced, but the universe’s expansion was the domineering process ensuring the net entropy increase.

There also was some debate here as to whether entropy can consistently be viewed as a measure of disorder. I am inclined to think that within the framework of physics, entropy indeed can be quite consistently viewed this way (see my essay here). Some physicists disagree. As to biology, I have no firm opinion — I just do not feel qualified to pass a judgment on this point. The questions of, say, entropy change in the process of protein molecules’ folding, may pose a problem to such an equating of entropy and disorder, but I am not prepared to say anything definite about this.

Regarding Robert’s comment stating the Clausius equation was good only for reversible processes, it is correct. While I did not write a subscript “rev” for dQ, I thought my text was clear enough to imply this was dQrev.

So, good luck to all — I am going to close comments to this thread.

About this Entry

This page contains a single entry by Mark Perakh published on January 2, 2006 10:09 PM.

Letter to the St. Petersburg Times on ID Poll was the previous entry in this blog.

Ken Miller in Cleveland: WEBCAST ARCHIVE URLS is the next entry in this blog.

Find recent content on the main index or look in the archives to find all content.



Author Archives

Powered by Movable Type 4.381

Site Meter