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Entropy
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Gibbs Paradox 2018
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Gibbs Paradox 2018

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

Deadline for manuscript submissions: closed (30 March 2018) | Viewed by 30646

Special Issue Editors

Prof. Dr. Dennis Dieks

E-Mail Website
Guest Editor
Descartes Centre, Utrecht University, Utrecht, The Netherlands
Interests: philosophy of physics; foundations of quantum mechanics; philosophy of space and time; probability; philosophy of science
Prof. Dr. Simon Saunders

E-Mail Website
Guest Editor
Philosophy of Physics, University of Oxford, Oxford, UK
Interests: foundations of quantum mechanics; symmetries and spacetime; relativistic quantum theory; philosophy of science; metaphysics

Special Issue Information

Dear Colleagues,

The Gibbs paradox, first intimated by J. Willard Gibbs in 1875, has proven to be remarkably durable. Its longevity may derive from on-going controversies in the foundations of quantum mechanics, or it may reflect its variegated nature: Not one paradox, but several. Essays are invited on any aspect of the paradox, but particularly those that reflect on its history, or that relate it to the nature of microphysical reality, or that otherwise explain why it remains controversial.

Prof. Dr. Dennis Dieks
Prof. Dr. Simon Saunders
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Gibbs paradox
  • entropy of mixing
  • indistinguishability
  • identical particles
  • foundations of statistical mechanics
  • quantum ontology

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Published Papers (5 papers)

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Research

24 pages, 1019 KiB  
Article
The Gibbs Paradox
by Simon Saunders
Entropy 2018, 20(8), 552; https://doi.org/10.3390/e20080552 - 25 Jul 2018
Cited by 14 | Viewed by 6083
Abstract
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there [...] Read more.
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs’ notion of ‘generic phase’). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction. Full article
(This article belongs to the Special Issue Gibbs Paradox 2018)
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15 pages, 262 KiB  
Article
The Gibbs Paradox and Particle Individuality
by Dennis Dieks
Entropy 2018, 20(6), 466; https://doi.org/10.3390/e20060466 - 15 Jun 2018
Cited by 9 | Viewed by 5221
Abstract
A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not, [...] Read more.
A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not, and the associated harmless discontinuity from “yes” to “no” is responsible for the discontinuity. By contrast, the Gibbs paradox in statistical physics continues to attract attention. Here, the problem is that standard calculations in statistical mechanics predict a non-vanishing value of the entropy of mixing even when two gases of the same kind are mixed, in conflict with thermodynamic predictions. This version of the Gibbs paradox is often seen as a sign that there is something fundamentally wrong with either the traditional expression S=klnW or with the way W is calculated. It is the aim of this article to review the situation from the orthodox (as opposed to information theoretic) standpoint. We demonstrate how the standard formalism is not only fully capable of dealing with the paradox, but also provides an intuitively clear picture of the relevant physical mechanisms. In particular, we pay attention to the explanatory relevance of the existence of particle trajectories in the classical context. We also discuss how the paradox survives the transition to quantum mechanics, in spite of the symmetrization postulates. Full article
(This article belongs to the Special Issue Gibbs Paradox 2018)
16 pages, 298 KiB  
Article
Probability, Entropy, and Gibbs’ Paradox(es)
by Robert H. Swendsen
Entropy 2018, 20(6), 450; https://doi.org/10.3390/e20060450 - 9 Jun 2018
Cited by 12 | Viewed by 4524
Abstract
Two distinct puzzles, which are both known as Gibbs’ paradox, have interested physicists since they were first identified in the 1870s. They each have significance for the foundations of statistical mechanics and have led to lively discussions with a wide variety of suggested [...] Read more.
Two distinct puzzles, which are both known as Gibbs’ paradox, have interested physicists since they were first identified in the 1870s. They each have significance for the foundations of statistical mechanics and have led to lively discussions with a wide variety of suggested resolutions. Most proposed resolutions had involved quantum mechanics, although the original puzzles were entirely classical and were posed before quantum mechanics was invented. In this paper, I show that contrary to what has often been suggested, quantum mechanics is not essential for resolving the paradoxes. I present a resolution of the paradoxes that does not depend on quantum mechanics and includes the case of colloidal solutions, for which quantum mechanics is not relevant. Full article
(This article belongs to the Special Issue Gibbs Paradox 2018)
54 pages, 1965 KiB  
Article
The Gibbs Paradox: Early History and Solutions
by Olivier Darrigol
Entropy 2018, 20(6), 443; https://doi.org/10.3390/e20060443 - 6 Jun 2018
Cited by 14 | Viewed by 8336
Abstract
This article is a detailed history of the Gibbs paradox, with philosophical morals. It purports to explain the origins of the paradox, to describe and criticize solutions of the paradox from the early times to the present, to use the history of statistical [...] Read more.
This article is a detailed history of the Gibbs paradox, with philosophical morals. It purports to explain the origins of the paradox, to describe and criticize solutions of the paradox from the early times to the present, to use the history of statistical mechanics as a reservoir of ideas for clarifying foundations and removing prejudices, and to relate the paradox to broad misunderstandings of the nature of physical theory. Full article
(This article belongs to the Special Issue Gibbs Paradox 2018)
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16 pages, 249 KiB  
Article
The Gibbs Paradox: Lessons from Thermodynamics
by Janneke Van Lith
Entropy 2018, 20(5), 328; https://doi.org/10.3390/e20050328 - 30 Apr 2018
Cited by 4 | Viewed by 4242
Abstract
The Gibbs paradox in statistical mechanics is often taken to indicate that already in the classical domain particles should be treated as fundamentally indistinguishable. This paper shows, on the contrary, how one can recover the thermodynamical account of the entropy of mixing, while [...] Read more.
The Gibbs paradox in statistical mechanics is often taken to indicate that already in the classical domain particles should be treated as fundamentally indistinguishable. This paper shows, on the contrary, how one can recover the thermodynamical account of the entropy of mixing, while treating states that only differ by permutations of similar particles as distinct. By reference to the orthodox theory of thermodynamics, it is argued that entropy differences are only meaningful if they are related to reversible processes connecting the initial and final state. For mixing processes, this means that processes should be considered in which particle number is allowed to vary. Within the context of statistical mechanics, the Gibbsian grandcanonical ensemble is a suitable device for describing such processes. It is shown how the grandcanonical entropy relates in the appropriate way to changes of other thermodynamical quantities in reversible processes, and how the thermodynamical account of the entropy of mixing is recovered even when treating the particles as distinguishable. Full article
(This article belongs to the Special Issue Gibbs Paradox 2018)
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