# Gibbs volume entropy is incorrect.

@article{Swendsen2015GibbsVE,
title={Gibbs volume entropy is incorrect.},
author={Robert H. Swendsen and Jian-Sheng Wang},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2015},
volume={92 2},
pages={
020103
}
}
• Published 23 June 2015
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics
We show that the expression for the equilibrium thermodynamic entropy contains an integral over a surface in phase space, and in so doing, we confirm that negative temperature is a valid thermodynamic concept. This demonstration disproves the claims of several recent papers that the Gibbs entropy, which contains an integral over a volume in phase space, is the correct definition and that thermodynamics cannot be extended to include negative temperatures. We further show that the Gibbs entropy…
29 Citations
The question of negative temperatures in thermodynamics and statistical mechanics
• D. A. Lavis
• Physics
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
• 2019
The Stumbling Block of the Gibbs Entropy: the Reality of the Negative Absolute Temperatures
The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system there exists a function of the system extensive parameters, called entropy, defined for all equilibrium
Thermodynamics of finite systems: a key issues review
• R. Swendsen
• Physics
Reports on progress in physics. Physical Society
• 2018
This paper will show that standard thermodynamics, with some minor generalizations, is correct, and the alternative thermodynamics suggested by Hilbert, Hänggi, and Dunkel is not, and that negative temperatures are thermodynamically consistent.
Continuity of the entropy of macroscopic quantum systems.
• R. Swendsen
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2015
This paper analyzes and calculates the thermodynamic entropy for large but finite quantum mechanical systems and preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics.
The thermodynamic entropy of a macroscopic quantum system is a continuous function of energy
Abstract The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of
Resolving the debate about proposed expressions for the classical entropy
Despite well over a century of effort, the proper expression for the classical entropy in statistical mechanics remains a subject of debate. The Boltzmann entropy (calculated from a surface in phase
Critique of the Gibbs volume entropy and its implication
Dunkel and Hilbert, "Consistent thermostatistics forbids negative absolute temperatures," Nature Physics, {\bf 10}, 67 (2014), and Hilbert, H\"anggi, and Dunkel, "Thermodynamic laws in isolated

## References

SHOWING 1-10 OF 32 REFERENCES
Gibbs, Boltzmann, and negative temperatures
• Physics
• 2015
In a recent paper, Dunkel and Hilbert [Nat. Phys. 10, 67–72 (2014)] use an entropy definition due to Gibbs to provide a “consistent thermostatistics” that forbids negative absolute temperatures.
Statistical mechanics of colloids and Boltzmann’s definition of the entropy
The Boltzmann entropy as traditionally presented in statistical mechanics textbooks is only a special case and not BoltZmann's fundamental definition, which leads to consistent and correct statistical mechanics and thermodynamics.
Thermodynamic laws in isolated systems.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2014
A detailed comparison of the most commonly considered microcanonical entropy definitions shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws of thermodynamics simultaneously.
Gibbs' Paradox and the Definition of Entropy
Gibbs’ Paradox is shown to arise from an incorrect traditional deﬁnition of the entropy that has unfortunately become entrenched in physics textbooks, which predicts a violation of the second law of thermodynamics when applied to colloids.
Consistent thermostatistics forbids negative absolute temperatures
• Physics
• 2014
Over the past 60 years, a considerable number of theories and experiments have claimed the existence of negative absolute temperature in spin systems and ultracold quantum gases. This has led to
Construction of microcanonical entropy on thermodynamic pillars.
• M. Campisi
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2015
The prototypical example of a macroscopic collection of noninteracting spins in a magnetic field is illustrated, and it is shown that the Boltzmann entropy severely fails to predict the magnetization, even in the thermodynamic limit.
Thermodynamics and an Introduction to Thermostatistics
GENERAL PRINCIPLES OF CLASSICAL THERMODYNAMICS. The Problem and the Postulates. The Conditions of Equilibrium. Some Formal Relationships, and Sample Systems. Reversible Processes and the Maximum Work