Talk:Entropy/Archive 3

message: In his CalPoly discussion, Frank writes:
:In sharp contrast, information ‘entropy’ depends only on one factor, the probability factor, -k Σ[Pi log Pi], where k is an arbitrary constant that never is required to involve energy, as does kB.
I think there's a danger that this can be taken the wrong way.  As I tried to persuade Astrobayes earlier, there's no great significance to the fact that in Chemistry entropy is usually measured in Joules per Kelvin, and temperature in Kelvins, while Σ[Pi log Pi] is dimesnionless.  One can entirely equivalently work throughout with the dimensionless entropy σ = S / k, and the energy-scale temperature τ = kT.
Indeed, as I suggested to Astrobayes, σ and τ are in many ways the more natural quantities, interestingly as Frank's friend Harvey Leff also expored in a recent paper, "What if Entropy were Dimensionless?", Am. J. Phys. 67, 1114-1122 (1999).   Not only does it more naturally reflect that the multiplicity, which is fundamentally what underlies entropy, is fundamentally a dimensionless variable.  It also throws into relief that the crucial thing about temperature is the corresponding energy-scale quantity τ = kT.  This is the amount of energy you have to put in to a system in thermodynamic equilibrium to get a unit increase in its dimensionless entropy σ.  That energy is greater for hot systems than for cold systems: energy flows from hot to cold, so for the 2nd law to be obeyed, the energy you need to add to a cold system to get a unit increase in dimensionless entropy must cause less than a unit decrease in the dimensionless entropy of the hot system. So working with σ and τ makes it a little more transparent why the energy τ for an ensemble, defined by ðE/ðσ (nearest I could find to a partial derivative "d") is the fundamental measure of its temperature. 
To his credit, in what he wrote on the (archived) talk page, Frank adds a sentance that underlines this:  
:Further, merely substituting kB for k does not magically alter a probability of shuffled cards or tossed coins so that it becomes a thermodynamic entropy change
This is surely the point on no account to be obscured: one can freely move between S and σ, and back again, without losing (or gaining) any physical meaning.  There's nothing particularly special either way about choosing whether or not to include the extra factor kB, and therefore whether or not to work with S rather than σ.
:====Response====
::The foregoing is helpful in many ways. I, too, once thought and used an argument about thermo entropy having joules/K etc. But dimensions, in themselves are not significant, as you say. HOWEVER :-), it's the presence of ENERGY as the enabling aspect (component?) of a TWO-component totality of thermodynamic entropy that implicitly/always MUST have 'joules/K' that IS the differentiation between thermodynamic entropy and ONE component informational 'entropy'.
::Thx for the pressing of the advantage of dimensionless sigma -- better than the understanding that I had. Excellent way -- for thermal physics that already has sigma front and center -- to prove 'hot to cold' is the 2nd law way! (For years, to show kids how obvious it is that energy dispersal from a hotter system to a cooler is the only way a positive entropy change occurs was using q/T [bold  for large number for T] (for ΔS, hotter)to q/T  [smaller number for T] (for ΔS, cooler).
 
::Also, although I salute Harvey re his dimensionless categorization of substances, since discovering 'dispersal', I've pushed viewing standard entropy values, and by yelling! that they must only be considered grossly/approximately/relative values of 'the energy that has incrementally been supplied the substance from 0 K to 298.15 K so that a particular substance could exist in that state' -- give far wider (and deeper) meaning to dozens of comparisons rather than just the old generalities about So differences in solid vs. liquid vs. gas. [Only way I beat Harvey!])  FrankLambert 20:21, 8 July 2006 (UTC)
thread_title:  1. kB 

message: The essence of Clausius’ original words are in the above paragraph. They differ somewhat from the version in the present Wikipedia ‘Entropy’ article, because (as shown below ) my statements use the German of his 1865 paper, cited in an authoritative history “The World of Physical Chemistry” by Keith Laidler (Oxford, 1993, p. 104-105):
“…schlage ich vor, die Grösse S nach dem griechischen Worte ή  τροπη [trope], die Verwandlung, die Entropie des Körpers zu nennen.  Das Wort Entropie habe ich absichtlich dem Worte Energie möglichst ähnlich gebildet, den die beiden Grössen, welche durch diese Worte benannt werden sollen, sind ihren physikalischen Bedeutungen nach einander so nahe verwandt, dass eine gewisse Gleichartigkeit in der Benennung mir zweckmässig zu sein scheint.”
 contributed by: FrankLambert 20:25, 9 July 2006 (UTC)
replies: text: Also, today I was at the sacred library collection at UIC and I read through an original copy of Clausius’ Mechanical Theory of Heat (365 pages) containing his nine memoirs (1850-1865), and thus I added the original 1854 mathematical statement of entropy word-for-word, so there is no confusion as to how this concept first started.--Sadi Carnot 11:12, 11 July 2006 (UTC)
thread_title: Explanation To The Group ( not part of article)

message: Wikipedia:WikiProject_Chemistry currently rates this article as "needs more chemistry to go with the physics"  (note: rating is not necessarily that recent).
In progress, I think we're already discussing issues about the appropriate tone to make a friendlier article for P Chem students.  (And, what specifically in the article might make it seem less friendly, or even alien to P Chem students).
But what *topics* should Physical Chemistry students expect to find presented here, that aren't already (and/or in breakout articles from here) ?
eg:
* Standard entropies (=> molar quantities, measured at stp, etc).
* Relationship with ΔG°, spontaneous and non-spontaneous reactions etc.
* Relationship with Equilibrium constants.
* Frequent assumption of more-or-less independence of ΔS with temperature.
* Trends in ΔS in chemical groups for particular sorts of reactions (eg ion solvation ...)
* Entropy effects in eg boiling point elevation, freezing point depression, ...
...
Actually, I suspect very little of that on this page, which is mostly signposts to more detailed articles; but perhaps more detail in an Entropy in Chemistry page, or handed off to Chemical Thermodynamics; or in individual relevant pages.
Part of the problem is that (IMO) Wikipedia needs a big push in the whole subject area of Physical Chemistry.  The whole P Chem subject area seems a lot less developed, so (as a comparative outsider) I find it hard to find out what needs the Entropy article needs to supply.
Hence this talk subject to try to get discussion going.  (And a plea at WP:Project Chemistry for an actively managed initiative to try to push quality in the whole field). Jheald 19:35, 10 July 2006 (UTC)
thread_title:  What needs to be added for Chemists ? 

message: To elaborate further on the preceding discussions, I particularly do not like individuals who purposely strive to alter historical frameworks of concept, in such a manner as to substitute their own personal contrivances for the original.  Owing to this conviction, today I was again down at the sacred copies room at the UIC library typing up, word-for-word, the original formulation of entropy, as it was intended to be stated.  The entire framework of entropy is built on some 365 pages worth of logical argument presented in nine memoirs over the course of 15 years, from 1850 to 1865.  Below are the main points of the way entropy was presented to the world in 1862-65 (starting from pg. 218 of Clausius' Mechanical Theory of Heat [the third page of the sixth memoir]):
The theorem respecting the equivalence-values of the transformations may accordingly be stated thus: The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.	The mathematical expression for this theorem is as follows.  Let dQ be an element of the heat given up by the body to any reservoir of heat during its own changes, heat which it may absorb from a reservoir being here reckoned as negative, and T the absolute temperature of the body at the moment of giving up this heat, then the equation:
:\int \frac {dQ} {T} \ = 0
must be true for every reversible cyclical process, and the relation:
:\int \frac {dQ} {T} \ \ge 0
must hold good for every cyclical process which is in any way possible.
	Although the necessity of this theorem admits of strict mathematical proof if we start from the fundamental proposition above quoted, it thereby nevertheless retains an abstract form, in which it is with difficulty embraced by the mind, and we feel compelled to seek for the precise physical cause, of which this theorem is a consequence.
(skipping a few paragraphs; Clausius then states the following law (as he calls it)):
In all cases in which the heat contained in a body does mechanical work by overcoming resistances, the magnitude of the resistances which it is capable of overcoming is proportional to the absolute temperature.
	In order to understand the significance of this law, we require to consider more closely the processes by which heat can perform mechanical work.  These processes always admit of being reduced to the alteration in some way or another of the arrangement of the constituent parts of the body.  For instance, when bodies are expanded by heat, their molecules being thus separated from each other: in this case the mutual attractions of the molecules on the other one had, and external opposing forces on the other, in so far as any are in operation, have to be overcome.
(skipping a paragraph)
In the cases first mentioned, the arrangements of the molecules is altered.  Since, even which a body remains in the same state of aggregation, its molecules do not retain fixed in varying position, by are constantly in a state of more of less extended motion, we may, when speaking of the arrangement of the molecules at any particular time, understand either the arrangement which would result from the molecules being fixed in the actual position they occupy at the instant in question, or we may suppose such an arrangement that each molecule occupies its mean position.  Now the effect of heat always tend to loosen the connexion between the molecules, and so to increase their mean distances from one another.  In order to be able to represent this mathematically, we will express the degree in which the molecules of a body are separated from each other, by introducing a new magnitude, which we will call the disgregation of the body, and by help of which we can define the effect of heat as simply tending to increase the disgregation.
(skipping about 20 pages)
I believe, indeed, that we must extend the application of this law, supposing it to be correct, still further, and especially to chemical combinations and decompositions.
	The separation of chemically combined substances is likewise an increase of the disgregation, and the chemical combination of previously isolated substances is a diminution of their disgregation; and consequently these processes may be brought under considerations of the same class as the formation or precipitation of vapour.  That in this case also the effect of heat is to increase the disgregation, results from many well-known phenomena, many compounds being decomposable by heat into their constituents—as, for example, mercuric oxide, and, at very high temperatures, even water.  To this it might perhaps be objected that, in other case, the effect of increased temperature is to favor the union of two substances—that, for instance, hydrogen and oxygen do not combine at low temperatures, but do so easily at higher temperatures.  I believe, however, that the heat exerts her only a secondary influence, contributing to bring the atoms into such relative positions that their inherent forces, by virtue of which they strive to unite, are able to come into operation.  Heat itself can never, in my opinion, tend to produce combination, but only, and in every case, decomposition.
(Then starting from page 354 of the ninth memoir is where he assigns the symbol S and gives it the name “entropy”)
The other magnitude to be here noticed is connected with the second fundamental theorem, and is contained in equation (IIa).  In fact if, as equation (IIa) asserts, the integral 
:\int \frac {dQ} {T} \ 
Vanishes whenever the body, starting from any initial condition, returns thereto after its passage through any other conditions, then the expression dQ/T under the sign integration must be the complete differential of a magnitude which depends only on the present existing condition of the body, and not upon the way by which t reached the latter.  Denoting his magnitude by S, we can write
: dS = \int \frac {dQ} {T} \ 
or, if we conceive this equation to be integrated for any reversible process whereby this body can pass from the selected initial condition to its present one, and denote at the same time by So the value which the magnitude S has in that initial condition,
: S = S_o + \int \frac {dQ} {T} \ 
This equation is to be used in the same way for determining S as equation (58) was for defining U.  The physical meaning of S has already been discussed in the Sixth Memoir.
(Then after a page of derivations, which includes a symbol assignment of disgregation, we then arrive back at the following equation)
we obtain the equation
: \int \frac {dQ} {T} \ = S - S_o 
We might call S the transformation content of the body, just as we termed the magnitude U its thermal and ergonal content.  But as I hold it to be better terms for important magnitudes from the ancient languages, so that they ay be adopted unchanged in all modern languages, I propose to call the magnitude S the entropy of the body, from the Greek word τροπη, transformation.  I have intentionally formed the word entropy so as to be as similar as possible to the word energy; for the two magnitudes to be denoted by these words are so nearly allied their physical meanings, that a certain similarity in designation appears to be desirable.
(Then, in grand finale of this equation-packed magnificent book, we arrive at his famous last paragraph on the last page [pg. 365] of ninth memoir, first presented to the public as sourced below*)
For the present I will confine myself to the statement of one result.  If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat:
#The energy of the universe is constant.
#The entropy of the universe tends to a maximum.
*(Ninth memoir): Read at the Philosophical Society of Zurich on the 24th of April, 1865, published in the Vierteljahrsschrift of this society, Bd. x. S. 1.; Pogg. Ann. July, 1865, Bd. cxxv. S. 353; Journ. de Liouville, 2e ser. t. x. p. 361. 
So there you have it.  I hope this gets us all on the same page so that there is no more talk-page bickering regarding fictitious concepts that were never presented in the words of Clausius.  Adios: --Sadi Carnot 04:23, 13 July 2006 (UTC)
thread_title: Entropy as defined by Clausius in 1862

message: Given this edit by Sadi Carnot (which is a valid edit, btw) I propose we move this article (i.e., renasme) to "Entropy (thermodynamics)" and remove anything unrelated to thermodynamics as the other uses are not in keeping with the thermodynamic meaning of entropy, and as they have their own articles. •Jim62sch• 16:27, 6 August 2006 (UTC)
replies: text: Since the term "entropy" is used mostly in the context of thermodynamics (and statistical mechanics), I'd suggest that the name of the article stays simply "Entropy", rather than "Entropy (thermodynamics)". I don't think anything should be removed from the article. All the other uses of this term are mentioned only briefly, which is good, since they are not unrelated to the thermodynamical entropy. Yevgeny Kats 19:12, 6 August 2006 (UTC)
replies: text: Since there is an entropy disambiguation page, I wouldn't recommend it.  I've always found that moving pages in Wikipedia creates more tension than it's worth. Olin 14:04, 7 August 2006 (UTC)

text: Because it's not like one word which incidentally has two different meanings, but these concepts are related. Yevgeny Kats 23:51, 7 August 2006 (UTC)
thread_title: Move

message: Note: This article has a small number of in-line citations for an article of its size and currently would not pass criteria 2b.
Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 00:19, 26 September 2006 (UTC)
thread_title:  GA Re-Review and In-line citations 

message: Two important consequences are that heat cannot of itself pass from a colder to a hotter body
: First of all, this is a statistical effect, so the theory really states that it is statistically improbable for this to occur.  Second of all, heat does flow from colder to warmer bodies spontaneously (through all of the usual mechanisms), it just so happens that more flows in the other direction.  It is like a chemical reaction that is reversible but biased.  Yes, this is a ridiculous nitpick, but seriously is it impossible to get more accurate wording here?  It's not like there's a magic one-way valve that prevents a colder object from radiating towards a warmer object - indeed the amount of this radiation is terribly important in many calculations involving heat shielding, etc.  -- JustinWick 01:03, 27 September 2006 (UTC)
replies: text: I feel your pain on this one and not too long ago I tried, vehemently, to get momentum going for an article improvement to address problems such as you raise here.  The result was that my edits and comments (and those of other users such as Frank Lambert) were hotly contested by a select few individuals and were usually changed.  I have left this article alone until the embers cooled a bit.  Perhaps we can look into an SPR in the near future?  Many physics articles have been discussed on SPR recently and have gained a lot of positive ground.  And doing so would involve a community of individuals with an interest in the physical accuracy of this article, rather than a point of view.  Cheers, Astrobayes 03:16, 27 September 2006 (UTC)
replies: text: I don't think its a ridiculous nitpick. However, I doubt that South Park Republicans (SPR) have anything to do with entropy. PAR 04:44, 27 September 2006 (UTC)

text: Firstly, sounds like an important correction to me: presumably it should read "are that it is statistically improbable fo heat of itself". Secondly, when I looked back at this page for info it had once again lapsed into the incomprehensibility that does so much to add to the mystique of entropy, but does nothing to explain it to beginners. I've therefore added a citation from  Frank Lambert to the intro, which in my opinion helps to make the article understandable. ...dave souza, talk 08:40, 27 September 2006 (UTC)
thread_title:  Utterly ridiculous nitpick