Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Is Classical Statistical Mechanics Self-Consistent?

P. Enders

Published Jan 1, 2007• 2 citations
OpenAlex

Abstract

In addition to his outstanding achievements in physics and activities in policy,C.-F. von Weizsacker is famous for his talks, given as a member of the Academy¨Leopoldina. Due to the latter, I could learn quite a lot from his methodologicalwritings. In particular, he is the only modern thinker I’m aware of who has pointedto the difference between Newton’s and Laplace’s notions of state. But this differenceis essential for the relationship between classical and quantum physics. Moreover it isthe clue to overcoming Gibbs’ paradox within classical statistical mechanics itself.

Related papers

Is Classical Statistical Mechanics Self-Consistent? (A paper in honour of C. F. von Weizsacker, 1912-2007)

P. Enders

Progress in physics•Jul 1, 2007•3 citations

Introduction

Jeffrey Olafsen

The issue is that one may enter an upper level course on statistical and thermal physics with only an appreciation of the classical macroscopic view never having attached quantum mechanics to anything thermodynamic. Statistical mechanics makes accurate predictions about systems which may contain 1023 or more particles. A sense of disbelief may be partly responsible for the widely held, but, incorrect view that statistical mechanics has to be difficult. A true understanding of entropy only comes from the microscopic treatment of the quantum approach made by statistical mechanics. The more fundamental, issue is that classical statistical mechanics is internally inconsistent, and can only be made to work by the importation from quantum theory of non-classical ideas such as indistinguishability. Gibbs’ paradox, over which the classical books agonize at length, vanishes into thin air in the quantum approach.

CRC Press eBooks•Jul 26, 2019•0 citations

Probability, Entropy, and Gibbs’ Paradox(es)

Robert H. Swendsen

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.

Entropy•Jun 9, 2018•19 citations

Representative Ensembles in Statistical Mechanics

Vyacheslav I. Yukalov

The notion of representative statistical ensembles, correctly representing statistical systems, is strictly formulated. This notion allows for a proper description of statistical systems, avoiding inconsistencies in theory. As an illustration, a Bose-condensed system is considered. It is shown that a self-consistent treatment of the latter, using a representative ensemble, always yields a conserving and gapless theory.

•Aug 3, 2013•22 citations

The Logic of Identity: Distinguishability and Indistinguishability in Classical and Quantum Physics

Dennis Dieks

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a ‘quantum connection’ stubbornly persists in the literature, even though it has also been criticized frequently. Here we shall argue that although this criticism is justified, the proposed alternative solutions have often been wrong and have not put the paradox in its right perspective. In fact, the Gibbs paradox is unrelated to fundamental issues of particle identity; only distinguishability in a pragmatic sense plays a role (in this we develop ideas of van Kampen [10]), and in principle the paradox always is there as long as the concept of a particle applies at all. In line with this we show that the paradox survives even in quantum mechanics, in spite of the quantum mechanical (anti-)symmetrization postulates.

•May 13, 2014•12 citations

The Gibbs Paradox: Lessons from Thermodynamics

Janneke van Lith

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.

Entropy•Apr 30, 2018•8 citations
In addition to his outstanding achievements in physics and activities in policy,C.-F. von Weizsacker is famous for his talks, given as a member of the Academy¨Leopoldina. Due to the latter, I could learn quite a lot from his methodologicalwritings. In particular, he is the only modern thinker I’m aware of who has pointedto the difference between Newton’s and Laplace’s notions of state. But this differenceis essential for the relationship between classical and quantum physics. Moreover it isthe clue to overcoming Gibbs’ paradox within classical statistical mechanics itself.
The issue is that one may enter an upper level course on statistical and thermal physics with only an appreciation of the classical macroscopic view never having attached quantum mechanics to anything thermodynamic. Statistical mechanics makes accurate predictions about systems which may contain 1023 or more particles. A sense of disbelief may be partly responsible for the widely held, but, incorrect view that statistical mechanics has to be difficult. A true understanding of entropy only comes from the microscopic treatment of the quantum approach made by statistical mechanics. The more fundamental, issue is that classical statistical mechanics is internally inconsistent, and can only be made to work by the importation from quantum theory of non-classical ideas such as indistinguishability. Gibbs’ paradox, over which the classical books agonize at length, vanishes into thin air in the quantum approach.
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.
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a ‘quantum connection’ stubbornly persists in the literature, even though it has also been criticized frequently. Here we shall argue that although this criticism is justified, the proposed alternative solutions have often been wrong and have not put the paradox in its right perspective. In fact, the Gibbs paradox is unrelated to fundamental issues of particle identity; only distinguishability in a pragmatic sense plays a role (in this we develop ideas of van Kampen [10]), and in principle the paradox always is there as long as the concept of a particle applies at all. In line with this we show that the paradox survives even in quantum mechanics, in spite of the quantum mechanical (anti-)symmetrization postulates.
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.