E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Special Issue "Gibbs Paradox and Its Resolutions"

Quicklinks

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (30 November 2009)

Special Issue Editor

Guest Editor
Dr. Theo M. Nieuwenhuizen (Website)

Institute for Theoretical Physics Visitors: Science Park 904, 1098 XH, Amsterdam
Fax: +31 20 5257675
Interests: foundations of general relativity; sub-quantum mechanics; quantum information theory; quantum measurement process; quantum thermodynamics and the Gibbs paradox; Biophysics: molecular motors; neural networks; DNA adsorption; black hole thermodynamics; black hole information paradox; Gravitation: globular star clusters; thermodynamic description of the glassy state; spin glasses and model glasses; transport of light in strongly scattering media; interfaces and directed polymers; lifshitz and Griffiths singularities; noise in physical systems; random walks on random lattices; disordered chains; foundations of special relativity

Special Issue Information

Literature

A collection of journal papers on Gibbs Paradox is available at http://www.mdpi.org/lin/entropy/gibbs-paradox.htm.

Keywords

  • entropy of mixing
  • distinguishability and indistinguishability
  • similarity
  • symmetry number
  • phase separation
  • configurational entropy (also a related special issue "Configurational Entropy")

Related Special Issue

Published Papers (9 papers)

View options order results:
result details:
Displaying articles 1-9
Export citation of selected articles as:

Editorial

Jump to: Research, Review, Other

Open AccessEditorial Diversity and Entropy
Entropy 1999, 1(1), 1-3; doi:10.3390/e1010001
Received: 28 January 1999 / Accepted: 5 February 1999 / Published: 11 February 1999
Cited by 14 | PDF Full-text (8 KB) | HTML Full-text | XML Full-text
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)

Research

Jump to: Editorial, Review, Other

Open AccessArticle In Defense of Gibbs and the Traditional Definition of the Entropy of Distinguishable Particles
Entropy 2010, 12(8), 1936-1945; doi:10.3390/e12081936
Received: 21 December 2009 / Revised: 2 August 2010 / Accepted: 20 August 2010 / Published: 24 August 2010
Cited by 6 | PDF Full-text (198 KB) | HTML Full-text | XML Full-text
Abstract
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 [...] 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)
Open AccessArticle Gibbs’ Paradox and the Definition of Entropy
Entropy 2008, 10(1), 15-18; doi:10.3390/entropy-e10010015
Received: 10 December 2007 / Accepted: 14 March 2008 / Published: 20 March 2008
Cited by 19 | PDF Full-text (118 KB)
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 [...] 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)
Open AccessArticle Some Observations on the Concepts of Information-Theoretic Entropy and Randomness
Entropy 2001, 3(1), 1-11; doi:10.3390/e3010001
Received: 15 February 2000 / Accepted: 11 January 2001 / Published: 1 February 2001
Cited by 9 | PDF Full-text (130 KB)
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 [...] 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)
Open AccessArticle Entropy Calculation of Reversible Mixing of Ideal Gases Shows Absence of Gibbs Paradox
Entropy 1999, 1(2), 25-36; doi:10.3390/e1020025
Received: 2 February 1999 / Accepted: 16 May 1999 / Published: 23 May 1999
Cited by 2 | PDF Full-text (41 KB) | HTML Full-text | XML Full-text
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. [...] 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)

Review

Jump to: Editorial, Research, Other

Open AccessReview Thermodynamics of the System of Distinguishable Particles
Entropy 2009, 11(3), 326-333; doi:10.3390/e11030326
Received: 16 April 2009 / Accepted: 25 June 2009 / Published: 29 June 2009
Cited by 9 | PDF Full-text (120 KB)
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 [...] 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)

Other

Jump to: Editorial, Research, Review

Open AccessLetter Gibbs’ Paradox in the Light of Newton’s Notion of State
Entropy 2009, 11(3), 454-456; doi:10.3390/e11030454
Received: 10 July 2009 / Accepted: 3 September 2009 / Published: 7 September 2009
Cited by 3 | PDF Full-text (48 KB) | HTML Full-text | XML Full-text
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)
Open AccessCommentary Gibbs Paradox and the Concepts of Information, Symmetry, Similarity and Their Relationship
Entropy 2008, 10(1), 1-5; doi:10.3390/entropy-e10010001
Received: 13 March 2008 / Published: 17 March 2008
Cited by 14 | PDF Full-text (90 KB) | HTML Full-text | XML Full-text
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 [...] 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)
Open AccessDiscussion On the So-Called Gibbs Paradox, and on the Real Paradox
Entropy 2007, 9(3), 132-136; doi:10.3390/e9030133
Received: 12 July 2007 / Accepted: 17 September 2007 / Published: 21 September 2007
Cited by 10 | PDF Full-text (210 KB)
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)

Journal Contact

MDPI AG
Entropy Editorial Office
St. Alban-Anlage 66, 4052 Basel, Switzerland
entropy@mdpi.com
Tel. +41 61 683 77 34
Fax: +41 61 302 89 18
Editorial Board
Contact Details Submit to Entropy
Back to Top