Talk:Entropy/Archive 1

My opinion about the entropy page and possible changes to it
Surely the thermodynamic quantity described as entropy in this page is in fact the same as the older and more understandable quantity - Heat Capacity at constant volume. I would also like to split this page into two separate pages - one giving a view of entropy as a measure of 'disorder' or number of ways of arranging a system - i.e. the statistical treatment (most of the second half of the article) and a second giving a view of entropy as a thermodynamic quantity (i.e. heat capacity) as used in relation with enthalpies and free energies etc - maybe this would help those (see below) who found the page confusing. Any comments / ideas ? Yes/No to this idea? Is also can't help noticing that much of the mid section of this work is wrong - a possible source of confusion for readers? (specifically sections entitled measuring entropy and thermodynamic definition of entropy and sections following directly on from the these sections.) I think a lot of confusion stems from the unnecessary introduction of a new word entropy when the concept of heat capacity is more intuitive - do other people share this opinion?HappyVR 19:04, 11 February 2006 (UTC)


 * Regardless of whether your blurb is correct or valuable, it does not belong at the top of the article. Stop putting it there. -- Xerxes 21:58, 12 February 2006 (UTC)
 * I would have thought whether it is correct or valuble would be quite an important factor in deciding whether it should be included - if you cannot be bother to assertain that maybe you should not be removing just because it's at the top.
 * (re xerxes Have you got anything usefull to say or are you just concerned with leaving pages exactly as they are?) The 'blurb' does relate to the article - where do you suggest putting it?

May be you could find a better place for this missing infomation.HappyVR 22:30, 12 February 2006 (UTC)


 * Banner paragraphs across the top of an article saying "this article isn't the right way to think about things" tend not to be seen as 'encyclopaedic style'. Particularly not if the claims are not universally accepted.


 * The right way to go, with a mature article with a long edit history like this one, is to thrash out the individual claims on the talk page until there is general agreement; and then to fix the sore points in the main body text of the article as needed to make it reflect the revised general view.


 * Top-posting edits to the main article which just say "this article is wrong" will tend to be deleted quite promptly (and quite rightly, IMO). -- Jheald 01:25, 13 February 2006 (UTC).

Talk page needs cleaning
This talk page needs to have stuff dumped into an archive. Any dead arguments, or old and obsolete comments should be archived. Please move all the comments under one header, not only one. perhaps we can have one header that lists the headers in the archive. I've made a link to the non existant archive above. Fresheneesz 00:50, 9 December 2005 (UTC)

Vague criticism
Sometimes the article is frustratingly vague. In particular:

It doesn't always seem to distinguish between definitions (p=mv, by definition) and laws (momentum is conserved, by observation).

A thermodynamic transformation is defined as "a change in a system's thermodynamic properties, such as its temperature and volume" (emphasis added). What other properties are relevant? Is it a long list?

What does "equilibrium state" mean? Complete thermodynamic equilibrium--the entire system must be a single temperature and pressure throughout?

I'd work on it myself, but I'm too clueless. Jorend 05:18, 24 Apr 2005 (UTC)


 * The reason for the vagueness is that thermodynamics applies to lots of different systems, and the thermodynamic parameters relevant to one system may not make any sense in another system. For example, in the thermodynamics of gases we talk about pressure and volume, whereas in the thermodynamics of ferromagnetic systems we talk about magnetization and susceptibility. The concept of "pressure" (or even "volume") doesn't make any sense for magnetic systems, while magnetization doesn't make any sense when we are looking at ordinary gases. There are only a handful of parameters that are common to all thermodynamic systems -- temperature, energy, entropy, heat capacity, and so forth. -- CYD


 * Thanks for your comment, CYD, and thanks immensely for all your work on this article. I wonder if it might be worth adding two examples (a classic ideal gas one and a magnetic one) to illustrate what the ambiguity is all about.  I'm not sure who the target audience for this article is, but it would be quite frustrating to have it aimed completely over my head, as I'm actually an engineer by training and had a semester course in thermo! -- 24.147.43.253 00:08, 25 Apr 2005 (UTC)

An intuitive understanding of entropy
I read this article hoping to obtain an intuitive understanding of entropy. Didn't get it. And I don't think the problem is that the article is too "hard"; I don't think it would provide an intuitive grasp of the subject to any reader, however sophisticated. Maybe the topic is too hard. If nothing else, more examples (and examples less wedded to chemical engineering) would be welcome.

Perhaps it is unclear what I mean by "intuitive understanding". I mean the ability to answer questions like these:

Consider my coffee cup as a thermodynamic system. I drop an ice cube into it. How does this affect the entropy? I have introduced a big difference in temperature between two parts of the system, so the entropy decreases, right? But coming at it from a different direction, it seems as though I have added heat to the system, by adding matter to it: even though the ice is frozen, the ice molecules have some thermal energy. So the entropy increases, right?

Is entropy meaningful outside the context of thermodynamic machines? For example, is entropy defined at non-equilibrium states? (The article sort of gives the impression that it isn't. But lots of real-world systems are essentially never at equilibrium, so this would be a serious limitation.)

I'm not clear on how entropy, energy, and work are tied together. How exactly is entropy related to the ability to do work? The article states that when you reach the maximum entropy state, no more work can be done--states it, that is, but doesn't explain. What is meant by "can't do work"--can't do significant, macroscopic work?

Can a supply of energy be referred to as "ordered" (i.e., capable of doing work)? It seems by definition that heat is the only form of energy that increases entropy. Are all other forms of energy equally "ordered" as far as entropy is concerned? After some thought, my guess is that all other forms of energy can be used to do work; only thermal energy can become dispersed and unable to do work, and entropy is a function of the distribution of thermal energy in a system. Am I getting warm?

The article talks about entropy of a system in relation to work done by the system. What about work done within the system (as, by one part of the system on another part)? Perhaps an equivalent way to put this question would be: How does entropy relate to non-thermodynamic properties (like potential energy) of parts of a system? If my previous guess is right, the only effect on entropy is when activity within the system converts other sorts of energy to "waste heat".

Entropy is defined as a function of the state of a system. Does it make any sense to compare the entropy of one system to the entropy of some other system that contains entirely different matter? For example, which has greater entropy: your average rock; or an ice crystal of the same mass at the same temperature? Is the question meaningful?

Kindly don't answer the questions here, unless you just want to talk them through. Improve the article instead. Thanks! Jorend 05:18, 24 Apr 2005 (UTC)

Revocation of additional definition was incorrect.
Entropy is defined for an irreversible expansion as:

$$\triangle S_{universe}\ =\ \triangle S_{system}\ +\ \triangle S_{surroundings}$$

$$= q_{sys}/T\ +\ q_{surroundings}/T\ $$

$$= nRTln(V2/V1)/T\ + [-nRTln(V2/V1)]/T\ =\ 0\ for\ equilibrium.$$

$$=nRln(V2/V1)\ >\ 0 for\ irreversible\ process!$$ because delta $$S_{surroundings}$$ = 0 and $$q_{surroundings} = 0$$.

Therefore, $$\triangle S_{universe}\ =\ \triangle S_{system}\ +\ \triangle S_{surroundings} \ge 0.$$ -- Tygar


 * That is not a meaningful definition of entropy, since the entropy of the universe is an arbitrary quantity. In any case, your argument relies on several assumptions, such as the fact that entropy is a state function, derived from the original definition based on reversible transformations. The article does talk about the entropy change associated with irreversible transformations further down. -- CYD

Hmm, math seems to be borked right now, except for cached equations and text translations. Just in time for my big landing. Oh well. -- CYD

Counting of microstates
think you should mention that in classical statistical mechanics infinite states/coarse graining isn't a problem when you are talking about change in entropy because difference in logs = log of a ratio which can be looked at as a ratio of volumes in phase space or the limit of ratios using coarse graining. currently the statistical formula is introduced here but immediately implied to be useless without jumping to quantum considerations

I can't touch it because I'm a total wikinewbie and don't know anything about thermo either

wtf
this article not written very clearly at all. The definition of absolute temperature is especially sketchy, and I don't like how it comes a good ways after the concept is first mentioned. And according to the current definition of "microstate", it would seem that there's an infinite number of them in any case. A good physics article should be accessable to anyone with competent knowledge of math.


 * I'm not certain what your complaint about the temperature is. If you feel that you have a better way of presenting it, go ahead and give it a shot. Note that temperature is defined in terms of entropy in statistical mechanics, and vice versa in classical thermodynamics.


 * As for the microstates: this subject is closely linked to the theory of measurement in quantum mechanics, which is (AFAIK) still dimly understood. The number of microstates would be infinite if we stick strictly to classical statistical mechanics. You have to introduce a "cut-off" to get rid of the infinities, essentially saying that two microstates that are "close" enough to one another should be treated as the same state. In classical mechanics, there's no way to justify this procedure, so it's an entirely arbitrary (though not unreasonable) requirement. In quantum mechanics, you can partially justify it using the Heisenberg uncertainty principle. -- CYD


 * What is geometrical frustration?

Additions
sitearm 16:38, 26 July 2005 (UTC)
 * Added Section 3 "Intuition and Entropy" and subsection 3.1 "Entropy in Cosmology"
 * Added bullet definition recaps at top for: "thermal energy, thermal work, thermal entropy, statistical thermal entropy, principle of increasing entropy"

Page move
I'm not entirely sure what's happened here. The article is at Entropy, but Talk:Entropy redirects to Talk:Thermodynamic entropy. As far as I can see, the article used to be at Thermodynamic entropy; after Entropy was moved to Entropy (disambiguation), Thermodynamic entropy was moved to Entropy. Looks like the talk page was left behind. I'm going to delete the current Talk:Entropy (which is just, and has always been, a redirect) and move Talk:Thermodynamic entropy there to match the article. &mdash; Knowledge Seeker &#2470; 06:13, 12 May 2005 (UTC)

Deleted material
moved from User talk:CYD:

Dear CYD: I notice you removed several of my edits to the article on Entropy. I found this disconcerting. When I read your change history comments I find I dispute them. The entropy/cosmology connection including gravity and black holes is clearly presented in Penrose and I made a point of adding him to the references. Also "entropy as a measure of disorder" does NOT suffice when you also state it as a measure of work that cannot be done. The added definitions established the work connection. I am new to Wikipedia. You are the original author of this article. Does that mean that you may freely delete anything you disagree with, even if sources for the material are cited? sitearm 03:44, 27 July 2005 (UTC)


 * I may freely delete anything in the article if it is incorrect or misleading; so can you, or any other user of the Wikipedia. That's how the Wikipedia works.


 * There are two sections I deleted. The first was a "cliff's notes" discussion of what thermal energy is, what entropy is, etc., given in point form, and repeating material that's already in the article. I deleted it because it is redundant, and because it goes against the style of Wikipedia articles.


 * The second deleted section is a somewhat incoherent discussion of entropy and cosmology. On second reading, I think some of this material should be in the article, but it's pretty flawed as it's written. It poses the question of why the early universe had low entropy, then proceeds to talk about how entropy ends up in black holes, which is a non-sequituer because that has nothing to do with the low-entropy question. It is also unclear whether the role of gravity as increasing disorder was invented by Penrose, or merely presented by him in his book (I can't remember); generally, Wikipedia prefers to refer to primary sources rather than secondary sources. Also, Penrose's "humorous diagram" has nothing to do with anything. I'll see if I can restore some cleaned-up version of this section. -- CYD


 * OK, done. -- CYD


 * Alphabetized references (minor edit) Sitearm 04:34, 28 July 2005 (UTC)

Thank-You, CYD
The current version of this article is MUCH better than what had been here before, thanks to CYD. The article still needs minor work, but CYD has taken care of the major revisions it desperately needed.

I would suggest that this Talk page be archived, with only comments made after CYD's revision being kept. Ravenswood 20:29, July 31, 2005 (UTC)


 * Thanks. -- CYD


 * I respectfully disagree. The issues raised in this discussion page of ease of understanding have not been addressed. Sitearm 07:50, 1 August 2005 (UTC)


 * Please specify which issues you're referring to. There's a lot of questions on this page, and no easy way to sift-out which have and which have not been addressed. Thanks. Ravenswood 16:10, August 2, 2005 (UTC)

What to keep on Entropy Talk
Below are questions that I think are important to better understand entropy. These need to stay on Talk until addressed in the article. I am OK with the rest of the Talk material to be archived as proposed. Thank you for your patience. Sitearm 15:46, 3 August 2005 (UTC)
 * "How are entropy, energy, and work tied together? What is the difference between "heat" and "energy"? How does entropy relate to kinetic and potential energy of parts of a system?. How is entropy related to the ability to do work before and after thermal equilibrium? What is meant by "can't do work"?


 * (i) The relation between entropy, energy, and work are explained in excruciating detail in the section on thermodynamics. (ii) Heat is just an amount of energy transferred from one system to another; what's the point? (iii) There is no deep relation; the entropy concept applies to systems in which "kinetic energy" and "potential energy" are meaningless concepts (e.g. magnetic systems.) (iv) Also explained in the section of thermodynamics. (v) Touched upon in the section of thermodynamics; I'll see what I can do to clarify this point. -- CYD

I will look to again add a more narrative section on the relationships between entropy, energy, and work in a separate section from yours. Please feel free to clarify in it but not to outright delete it. I request you be accomodating to additional ways of describing mechanical entropy. What is clear and obvious to you in your exposition is not so to me. Let's at least get the narrative worked out before trying to collapse things. I have spent a lot of time reading the policy discussions in Village Pump and I am aware there are major edit revert wars going on in some of these pages. I am not interested in that. I am interested in a great article on Entropy. I am interested in following Wikiquette rules. A concerned newcomer Sitearm 07:48, 4 August 2005 (UTC)

Thermodynamic definition of entropy

 * $$\Delta S = \frac{\Delta Q}{T} \,\!$$

$$\Delta Q\!$$ notation is confusing. How is the heat changing? The heat article also has this notation in places

I changed this to simply be Q


 * Are you kidding? How is delta notation confusing, we learn about that starting in like 6th grade. And how can entropy (s) be changing if nothing in its equivelant expression ( &delta; Q / T) isn't changing??? If thats still not reverted i'm going to right now. Fresheneesz 00:53, 9 December 2005 (UTC)


 * I agree with this as well. Entropy change only makes sense if Energy is going into or coming out of that system.  The (Delta)Q has to stay - to do otherwise would diverge from what is a common definition in physics.  To answer your question specifically, the heat is changing any time the system at temperature T may interact with any other system thermally. C.Melton 01:40, 14 February 2006 (UTC)


 * To be more exact


 * $$\Delta S \ge \frac{\Delta Q}{T} \,\!$$


 * and REVERSIBLE entropy change only makes sense if energy is going into or coming out of that system. There can be entropy change without change in energy as in entropy of mixing. PAR 06:34, 14 February 2006 (UTC)


 * No, the correct definition is $$\Delta S \ge \frac{Q}{T} \,\!$$. There is no delta in front of the Q in this equation. 'Q' is the heat, the flow of thermal energy into the system from the environment. It is already a change in energy, so the delta is not needed. Nonsuch 22:27, 20 February 2006 (UTC)

definition of entropy
I removed the following,
 * In the limiting case of a reversible cycle consisting of a continuous sequence of transformations,


 * $$\oint \frac{dQ}{T} = 0 \,\!$$ (reversible cycles)


 * where the integral is taken over the entire cycle, and T is the temperature of the system at each point in the cycle.

because a heat engine rarely uses a continuum of temperatures, and because it is pointless.Bo Jacoby 11:28, 16 September 2005 (UTC)

I changed Q to dE everywhere, because 'heat' may either mean energy or entropy and so should not be used. Here Q was energy. I finished the definition of temperature, noting that the definition leaves the unit undefined. I hope you like it. Bo Jacoby 13:44, 16 September 2005 (UTC)

Entropy change in irreversible transformations

 * "We now consider irreversible transformations. The entropy change during any transformation between two equilibrium states is . . ."

Either show it or don't show it, but don't tell me that it is easy to show. I don't think it is easy to show. I don't even think it is correct. Throw a hot piece of iron into a bucket of water, and the entropy of the iron is diminished. . . Bo Jacoby 14:00, 16 September 2005 (UTC)


 * If you don't know how to go about proving or disproving the equation, you shouldn't be so quick to dismiss it as wrong. FYI, whatever the entropy change of your "hot piece of iron" is, it is necessarily greater than the integral of dQ/T (where dQ is negative if heat flows out of the system.) -- CYD

Lousy introduction
I've reverted the introduction to a previous version, because it's difficult to read and riddled with inaccuracies. The problems are too many to point out individually, but take for example


 * A little energy dE is transferred to a body of temperature T by means of a little entropy transfer dS

This is inaccurate because it assumes no change in volume or other extensive thermodynamic variables, an important assumption that's simply left unstated. Also, "entropy transfer" is not a meaningful concept, only "entropy change" -- entropy is a property of a thermodynamic system.

That whole discussion of "quantities of electricity" is almost unreadable, thanks to liberal use of inline TeX; luckily, it is also almost completely irrelevant, and can be safely deleted.

Incidentally, the article itself serves as a demonstration of the second law of thermodynamics. When I last looked at it a month ago, it was in pretty good shape. Since then, the amount of disorder has increased, and one has to do work to get it back to its original level of quality. -- CYD


 * Hello CYD. You disliked my changes. OK. I made them for a reason, but I accept that the author is not the sole judge of the quality of a text. Do you too ? I didn't say that dE is the energy change of the body. I said that it is the energy transferred to the body by means of the entropy transfer. This energy does not depend on whether the body transfers some energy further on to some third body by changing volume or other extensive thermodynamic variables. I disagree that entropy transfer is not a meaningsful concept. Entropy transfer (between bodies) must be understood before entropy content (as a property of a body) can be understood, because the zero-point of entropy transfer is well defined, while the zero-point of entropy content is arbitrary. Bo Jacoby 08:02, 6 October 2005 (UTC) (PS. Note that 4 ~ instead of 3 ~ will date your signature.)


 * Dunno what you mean by the "zero-point of entropy transfer", but the zero-point of the entropy of a system is perfectly well defined. That's the whole point of the zeroth law. -- CYD


 * If two bodies are thermally insulated from one another then they do not exchange entropy. So thermal insulation defines the zero point of entropy transfer. The zeroth law, which is historically later than the other laws, state that at zero temperature the entropy content of a body tend to a value, which is conventionary called zero. Bo Jacoby 13:16, 6 October 2005 (UTC)


 * Nope. The zeroth law states that the entropy of a system at zero temperature is a well-defined -- not arbitrary -- number, equal to the degeneracy of its quantum mechanical ground state. -- CYD


 * See Third law of thermodynamics. We were wrong regarding the numbering of laws. I agree that the log of the degeneracy of the ground state is the sensible definition of the zero-point of entropy, but still it is an arbitrary additional definition. The original definition of thermodynamic entropy leaves the zero point undefined. It just defines the increment dS. Bo Jacoby 13:20, 7 October 2005 (UTC)


 * That "arbitrary additional definition" happens to be the basis of the entire field of quantum statistical mechanics... -- CYD


 * Surely. But the question was concerning transfer of entropy, which you claim "is not a meaningful concept". Bo Jacoby 13:45, 7 October 2005 (UTC)


 * You're the one who brought up all that stuff about "zero point of entropy transfer", which we now see is irrelevant and wrong: "Entropy transfer (between bodies) must be understood before entropy content (as a property of a body) can be understood, because the zero-point of entropy transfer is well defined, while the zero-point of entropy content is arbitrary." In fact, it's entropy content that's well-defined, whereas entropy transfer is not meaningful because entropy is generally not a conserved quantity. -- CYD


 * I respectfully disagree. Entropy transfer dS=dQ/T was defined by heat transfer dQ and temperature T. It is shown that the integral of dS from a beginning state to a final state depend only on these two states and not on the intermediate states. Then the definition of entropy content is established. The concept of entropy transfer is logically prerequisite to the concept of entropy contents as a state function. As explained in the 'lousy' introduction of mine. If a thermal connection between bodies of temperatures T1 and T2 transfers the energy dE, the entropy taken from the hot body is dE/T2 and the entropy given to the cold body is dE/T1. The difference dE/T1-dE/T2 is created by the irreversible process of heat conduction. Until you know this, you cannot understand the concept of entropy content. Bo Jacoby 07:17, 10 October 2005 (UTC)

Entropy and disorder
I think the entropy and disorder section was getting a little wordy. The new addition was good in that it introduced the concept of Shannon entropy to the messy bedroom analogy, and I have tried to pare the argument in that section down to a simpler statement. PAR 18:39, 8 January 2006 (UTC)

Entropy - A new world view
About the reference to to the book "Entropy: A New World View". The article states it is "a notorious misinterpretation of entropy" and links to Foresight to prove it. But Foresight seems to be full of crap, they state that "Therefore, entropy can decline in a closed system", clearly not understanding what a closed system even is. How can you link to such an unreliable source? The book may over interpret some aspects of the law, but it still have a lot of good points and should not be categorical put down in that way. -- A human 14:21, 16 January 2006 (UTC)


 * I am afraid that you misunderstand Foresight. Actually, Rifkin does not understand what a closed system is. Foresight says "Rifkin declares that the Earth is a closed system, exchanging energy but not matter with its surroundings, and that therefore "here on earth material entropy is continually increasing and must ultimately reach a maximum," making Earth's life falter and die." And in the context of Rifkin's (wrong) closed system definition, Foresight says "Rifkin himself states that "in science, only one uncompromising exception is enough to invalidate a law." This thought experiment, which mimics how natural salt deposits have formed on Earth, invalidates the law on which he founds his whole book. So do plants. Sunlight brings energy from space; heat radiated back into space carries away entropy (of which there is only one kind). Therefore, entropy can decline in a closed system and flowers can bloom on Earth for age upon age." That is meant to prove that Rifkin is wrong. I think that Entropy: A New World View deserves a harsh treatment. Rifkin utterly failed to understand Entropy. -- Shotgunlee 03:11, 17 January 2006 (UTC)

Great article
This is a great article. I'm sure I would only make it worse if i were to try to add my two cents to it. but it would be nice if certain things were ummm aaa mentioned ... maybe dealt with .. maybe added to external links??
 * Potential energy
 * Useable energy
 * Gravity
 * Spacial distribution of energy
 * photons

I have in mind data stuff somewhat like:
 * 
 * 
 * 
 * 

Context: On evolution "entropy is limited to heat" was changed to "entropy is about useable energy" was changed to "entropy is about spacial distribution of energy" ... or something like that. WAS 4.250 03:46, 17 January 2006 (UTC)

Way too technical
I'm a non-scientist, and this may as well have been in urdu for all I could understand of it. Aren't these articles supposed to be understandable by the average joe like me? ElectricRay 23:29, 22 January 2006 (UTC)


 * I agree; I like that the article goes into detail, but it never comes from a nutshell, layman explanation. j_freeman 19:29, 24 January 2006 (UTC)


 * I made some attempt to construct a less technical front-end for the Information theory article, using some material that has served me well in the past for introducing the subject on more intuitive grounds. You may find it helpful.  Either way, let me know what you think.  Jon Awbrey 19:36, 24 January 2006 (UTC)

Laymen in college
This article is slightly better explained than the two courses I've taken in two different colleges, so its a pretty good explanation. Some people point out ambiguities and that's all good, but the point is driven home better than in most books and college courses. This is NOT an easy topic, and is, for most people, impossible to graps by skimming trough it. As for the current state of "this article doesn't say what the hell the topic (entropy) actually is."... I point to the line that reads: "Entropy is a measure of how far along this process of equalization has come." This, plus the equations, is all. The rest is only so you can grasp this phrase, that is found right in the introduction. Congratulations to whoever wrote this. As for the ice cube and entropy effect, I point to the article again: "the entropy of an isolated system can only increase or remain the same; it cannot decrease" And for delta-Q notation, removing it is a bad idea. Q usually means the heat contained in the system, and using this to notate heat transfers is confusing to those who use formal notation. Please, do not reinvent standard notation. Also, if you didn't take a formal class in the subject, please refrain from editing, as you probably don't grasp the concept fully. -Annoyed Wikipedia reader

disorder
I realize there's a long history about the word disorder, but I wonder if it would be better to rephrase it as "statistical disorder" or even "statistical randomness." Some sources have even abandon this and used "dispersion of energy." Olin


 * There's been a discussion about the word "disorder" and I don't think its completely resolved, because there is no mathematical definition of disorder, so it gets batted around back and forth. As far as "dispersion of energy" is concerned, that's wrong. In the case of entropy of mixing there is nothing that can be identified as a dispersion of energy, which goes to show that thinking of entropy as a dispersion of energy is wrong. PAR 19:29, 7 February 2006 (UTC)


 * Ah, but there is a dispersal of energy (or a change in the way the energy can be distributed), in my understanding. Here's a link to a Journal of Chemical Education article that explains it:  http://www.entropysite.com/calpoly_talk.html  The main site discusses it as well.  Olin


 * The article is kind of confusing. The closest he comes to stating the case for entropy of mixing is:


 * The mixing of two different liquids (or solute in solvent) is a more subtle spreading of each component’s energetic molecules, but clearly they become more separated from one another than when in the pure state they were colliding only with identical adjacent molecules.


 * This is physical spreading, not energy spreading.


 * If you have a box divided in two by a partition, with type A gas on one side, type B on the other, same mass per particle, same temperature and pressure, then there will be no change in the energy density when the partition is removed and the gases mix, but there will be an increase in entropy. You could say that the energy held by gas A gets spread out, as does the energy held by gas B, but I don't think it is productive to think of energy as being "owned" by a particular molecule type. Energy is being exchanged at every collision, its not "owned" by any gas. PAR 03:18, 8 February 2006 (UTC)


 * After reading the Wiki article and the archive talk section, I agree the article here is OK. And while I understand your reasoning, there has to be more microstates accessed since S = k ln W.  I agree with you that the dispersal of energy is probably a bad term for this, but more disordered is misleading, too.  In reality, the density of states has changed; does this really mean that the system is "more disordered"? Olin


 * My view on the "disorder" subject is that "disorder" is not a technical term, it is a term used to help people get an intuitive understanding of entropy. As a rough general statement, there are many more ways to have a "disordered" situation than there are to have an "ordered" situation, and this is the qualitative link between disorder and entropy. Since "disorder" is not a technical term, it is imprecise and not very useful once one sits down and studies the true definition of entropy. It is useful as an introductory description, but its not productive to push the analogy too far. PAR 18:25, 8 February 2006 (UTC)


 * The problem is that disorder invariably does *not* help people gain intuition, and simply confuses *everyone* (even people that think they understand, or even those that actually do). This term MUST be specifically defined, since it is used so specifically in the terms of entropy. I have given sort of a definition of the term entropy in the intro. It'll probably be reverted or something, but I really think the term "disorder" was a collosal mistake, and simply makes entropy an easily confusing topic. I vote that we make *clear* note of the meaning of "disorder" and only use the term *sparingly* in this article. Comments? Fresheneesz 10:02, 4 April 2006 (UTC)

This sentence
"By the conservation of energy, the net energy lost by the environment is equal to the work done by the engine." looks some what vague.What say?--Sahodaran 05:25, 8 February 2006 (UTC)

Arrow of Time
How does entropy "pick" a direction in time? By my reasoning, statistically it should increase both into the future and into the past. A partially melted ice cube in a glass of water is far more likely to have been an unlikely perturbation in water molecules (a random jump to slightly lower entropy) than it is to have ever been a fully formed ice cube (an extremely lower entropy.) As I understand, the illusion of an arrow of time is based on an extremely low entropy early universe. Please discuss this.Adodge 23:04, 11 February 2006 (UTC)


 * As I understand it entropy doesn't 'pick' a direction - the two processes ie time increasing and entropy increasing both occur independantly - this gives the impression that entropy all ways increases with time - which is the correct impression to get. I hope that helps a bit.
 * Or as an alternative view: the natural increase in entropy (if you accept that disorder does naturally increase?) causes the arrow of time - because there never is an overall decrease in entropy? And so entropy becomes a measure of time and vice versa...(Maybe a better question would be - why do we think time is increasing.)HappyVR


 * You seem to be saying completely contradictory things in your two paragraphs here, HappyVR. The overwhelming experimental observation is that the Second Law of Thermodynamics holds.  So observationally we find that increasing entropy (at least for thermodyamically "large" systems, where fluctuations are negligible) defines an arrow of time.  Your first paragraph doesn't make any sense to me. -- Jheald 01:09, 13 February 2006 (UTC).


 * I think it should be noted that all living things - plants and animals - tend not to increase in entropy - we cause the entropy of our surroundings to increase - by breathing out hot air amongst other things - maybe this is why entropy seems such a difficult subject for people since we spend our lifes trying to prevent it happening to us.


 * As for a low entropy early universe I cannot say though it does seem to be a logical conclusion.


 * As for you middle-bit about the ice cube - I agree - so I think what your saying is that it is more likely for a glass of water to spontaneously form a partially melted ice cube than it is to spontaneously form a completely unmelted ice cube - is this right? - unlikely events can (and do occur) but for each unlikely event that occurs there will be many more likely events occuring? Also I would consider the difference between expectation (in a mathematical sense) and probability. HappyVR 23:49, 11 February 2006 (UTC)


 * No, he's saying that if you find a partially melted ice cube now, and ask not where is it going?, but rather where did it come from?, then statistical mechanics would tell you that most probably it should have started out as a completely unmelted glass of water, that had spontaneously happened to half freeze itself. In the absence of additional prior information about likely initial conditions, statistical mechanics would consider that less totally improbable, that an unmelted glass of water would spontaneously partially freeze itself, than that a fully frozen glass should have existed at all. -- Jheald 00:56, 13 February 2006 (UTC).

IMO, Adodge, you are exactly right. (Though I don't think I'd call the arrow of time an "illusion"). You might also like to look at the article MaxEnt thermodynamics, which comes to the same conclusion, that there is important "prior" information missing from the formalism at it stands if one is to address the retrodiction question (sometimes called "Boltzmann's 2nd Problem").

That article probably goes the furthest. The articles H-theorem and Loschmidt's paradox don't go quite as far, but both do address problems with the claim that "statistical mechanics proves that statistical entropy increases" &mdash; as the article on information theory currently puts it: "The theorem ((that statistical entropy should be always increasing)) relies on a hidden assumption, that useful information is destroyed by the collisions, which can be questioned; also, it relies on a non-equilibrium state being singled out as the initial state (not the final state), which breaks time symmetry; also, strictly it applies only in a statistical sense, namely that an average H-function would be non-decreasing)".

So, the supposed "proof" from within statistical mechanics begs the question. If entropy does increase, that is an observational fact which cannot be deduced just from the bare formalism - the prediction requires the injection of additional a-priori beliefs about the initial state. As you say, it presumably reflects an invariable experimental fact that thermodynamic systems, for some unspecified external reason, always start out in an unusually low-entropy initial state, about which the statistical mechanical formalism itself is entirely agnostic. (This may reflect particularly low-entropy initial state at the start of the universe. A slightly different take is that the number of available histories/non-identical microstates in the universe may be increasing, eg for some quantum or gravitational/cosmological reason).

Finally, it's worth noting that it's often argued that the psychological direction of time may be a completely dependent consequence of the entropic direction of time -- ie we would always define 'forward' time as the direction with increasing entropy, and then fix the labels on any graphs to match. All of this (should be!) discussed at greater length in the article Arrow of time. Hope this helps. -- Jheald 00:50, 13 February 2006 (UTC).

Excellent. Very illuminating. Thank you. Alex Dodge 08:45, 13 February 2006 (UTC) ???

Stub proposal
Anybody interested in joining to do a stub on the term: "corporate entropy"? I keep coming across the term in many places. For example, the (1999) 2nd Edition of the book Peopleware has a section on how to fight “corporate entropy”, Google shows all sorts of hits for the term, and you can find it used on many Blogs. Does anyone know the origin of this term, i.e. who coined it or first used it in application?--Sadi Carnot 19:00, 20 February 2006 (UTC)

Black holes & entropy
From the article:

''If the universe can be considered to have increasing entropy, then, as Roger Penrose has pointed out, an important role in the disordering process is played by gravity, which causes dispersed matter to accumulate into stars, which collapse eventually into black holes. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes.''

What effect does hawking radiation have on this? I'm specifically thinking of the fact that black holes are unstable, and have a limited lifetime - which either contradicts the second law of thermodynamics or the statement that black holes have the maximum possible entropy. Mike Peel 13:18, 17 March 2006 (UTC)