Entropy

198 KiB

Open AccessArticle

In Defense of Gibbs and the Traditional Definition of the Entropy of Distinguishable Particles

by John F. Nagle

Entropy 2010, 12(8), 1936-1945; https://0-doi-org.brum.beds.ac.uk/10.3390/e12081936 - 24 Aug 2010

Cited by 10 | Viewed by 7977

The traditional Gibbs’ calculation of the entropy of distinguishable classical particles that leads to Gibbs Paradox has been criticized recently. This criticism, if valid, would require a substantially different definition of entropy in general. However, the traditional definition of entropy works quite well [...] Read more.

The traditional Gibbs’ calculation of the entropy of distinguishable classical particles that leads to Gibbs Paradox has been criticized recently. This criticism, if valid, would require a substantially different definition of entropy in general. However, the traditional definition of entropy works quite well in situations where the distinguishability of classical particles is taken seriously while a suggested replacement definition fails. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

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118 KiB

Open AccessArticle

Gibbs’ Paradox and the Definition of Entropy

by Robert H. Swendsen

Entropy 2008, 10(1), 15-18; https://0-doi-org.brum.beds.ac.uk/10.3390/entropy-e10010015 - 20 Mar 2008

Cited by 39 | Viewed by 16244

Abstract

Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adopting [...] Read more.

Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adopting Boltzmann’s definition of the entropy, the violation of the second law is eliminated, the properties of colloids are correctly predicted, and Gibbs’ Paradox vanishes. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

8 KiB

Open AccessEditorial

Diversity and Entropy

by Shu-Kun Lin

Entropy 1999, 1(1), 1-3; https://0-doi-org.brum.beds.ac.uk/10.3390/e1010001 - 11 Feb 1999

Cited by 25 | Viewed by 10035

Abstract

Entropy has been launched as a scientific journal to provide an advanced forum for the community of entropy and information researchers. [...] Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

41 KiB

Open AccessArticle

Entropy Calculation of Reversible Mixing of Ideal Gases Shows Absence of Gibbs Paradox

by Vasili Tatarin and Oleg Borodiouk

Entropy 1999, 1(2), 25-36; https://0-doi-org.brum.beds.ac.uk/10.3390/e1020025 - 23 May 1999

Cited by 3 | Viewed by 12297

Abstract

We consider the work of reversible mixing of ideal gases using a real process. Now assumptions were made concerning infinite shifts, infinite number of cycles and infinite work to provide an accurate calculation of entropy resulting from reversible mixing of ideal gases. We [...] Read more.

We consider the work of reversible mixing of ideal gases using a real process. Now assumptions were made concerning infinite shifts, infinite number of cycles and infinite work to provide an accurate calculation of entropy resulting from reversible mixing of ideal gases. We derived an equation showing the dependence of this entropy on the difference in potential of mixed gases, which is evidence for the absence of Gibbs' paradox. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

130 KiB

Open AccessArticle

Some Observations on the Concepts of Information-Theoretic Entropy and Randomness

by Jonathan D.H. Smith

Entropy 2001, 3(1), 1-11; https://0-doi-org.brum.beds.ac.uk/10.3390/e3010001 - 01 Feb 2001

Cited by 20 | Viewed by 9848

Abstract

Certain aspects of the history, derivation, and physical application of the information-theoretic entropy concept are discussed. Pre-dating Shannon, the concept is traced back to Pauli. A derivation from first principles is given, without use of approximations. The concept depends on the underlying degree [...] Read more.

Certain aspects of the history, derivation, and physical application of the information-theoretic entropy concept are discussed. Pre-dating Shannon, the concept is traced back to Pauli. A derivation from first principles is given, without use of approximations. The concept depends on the underlying degree of randomness. In physical applications, this translates to dependence on the experimental apparatus available. An example illustrates how this dependence affects Prigogine's proposal for the use of the Second Law of Thermodynamics as a selection principle for the breaking of time symmetry. The dependence also serves to yield a resolution of the so-called ``Gibbs Paradox.'' Extension of the concept from the discrete to the continuous case is discussed. The usual extension is shown to be dimensionally incorrect. Correction introduces a reference density, leading to the concept of Kullback entropy. Practical relativistic considerations suggest a possible proper reference density. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

210 KiB

Open AccessDiscussion

On the So-Called Gibbs Paradox, and on the Real Paradox

by Arieh Ben-Naim

Entropy 2007, 9(3), 132-136; https://0-doi-org.brum.beds.ac.uk/10.3390/e9030133 - 21 Sep 2007

Cited by 20 | Viewed by 15157

Abstract

Two versions of the so-called Gibbs paradox are discussed. Both of these areshown to be non-paradoxes. It is also shown that there is a different real paradox that emergesfrom Gibbs writings. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

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90 KiB

Open AccessCommentary

Gibbs Paradox and the Concepts of Information, Symmetry, Similarity and Their Relationship

by Shu-Kun Lin

Entropy 2008, 10(1), 1-5; https://0-doi-org.brum.beds.ac.uk/10.3390/entropy-e10010001 - 17 Mar 2008

Cited by 18 | Viewed by 24291

Abstract

We are publishing volume 10 of Entropy. When I was a chemistry student I was facinated by thermodynamic problems, particularly the Gibbs paradox. It has now been more than 10 years since I actively published on this topic [1-4]. During this decade, [...] Read more.

We are publishing volume 10 of Entropy. When I was a chemistry student I was facinated by thermodynamic problems, particularly the Gibbs paradox. It has now been more than 10 years since I actively published on this topic [1-4]. During this decade, the globalized Information Society has been developing very quickly based on the Internet and the term information is widely used, but what is information? What is its relationship with entropy and other concepts like symmetry, distinguishability and stability? What is the situation of entropy research in general? As the Editor-in-Chief of Entropy, I feel it is time to offer some comments, present my own opinions in this matter and point out a major flaw in related studies. [...] Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

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120 KiB

Open AccessReview

Thermodynamics of the System of Distinguishable Particles

by Chi-Ho Cheng

Entropy 2009, 11(3), 326-333; https://0-doi-org.brum.beds.ac.uk/10.3390/e11030326 - 29 Jun 2009

Cited by 14 | Viewed by 12865

Abstract

The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to [...] Read more.

The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to the so-called Gibbs paradox in which the mixing entropy of two identical classical gases increases. Lots of literature from different points of view were created to resolve the paradox. In this paper, starting from the Boltzmann entropy, we present the thermodynamics of the system of distinguishable particles. A straightforward way to get the corrected Boltzmann counting is shown. The corrected Boltzmann counting factor can be justified in classical statistical mechanics. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

48 KiB

Open AccessLetter

Gibbs’ Paradox in the Light of Newton’s Notion of State

by Peter Enders

Entropy 2009, 11(3), 454-456; https://0-doi-org.brum.beds.ac.uk/10.3390/e11030454 - 07 Sep 2009

Cited by 6 | Viewed by 8612

Abstract

In this letter, it is argued that the correct counting of microstates is obtained from the very beginning when using Newtonian rather than Laplacian state functions, because the former are intrinsically permutation invariant. Full article

(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)

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