# Gibbs' Paradox and the Definition of Entropy

@article{Swendsen2008GibbsPA, title={Gibbs' Paradox and the Definition of Entropy}, author={Robert H. Swendsen}, journal={Entropy}, year={2008}, volume={10}, pages={15-18} }

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

## 43 Citations

The Gibbs Paradox and the Definition of Entropy in Statistical Mechanics

- PhilosophyPhilosophy of Science
- 2012

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: (i) the “classical” Boltzmann entropy (SB1); (ii) the modified Boltzmann…

About the Correlation and Physical Foundation of Thermodynamic and Information Entropy : Γ-Phase Space and the Impact to the Outer World Pedagogic Research

- Physics
- 2018

Although the term “Entropy S” has been introduced to thermodynamics by Clausius already in the 19th century and Boltzmann’s genius relation S = kB lnW that relates thermodynamics and statistics dates…

Physics of uncertainty, the Gibbs paradox and indistinguishable particles

- Computer Science
- 2013

Comments on the Extensivity of the Boltzmann Entropy

- Physics, Computer Science
- 2016

The Boltzmann entropy S as shown here for the ideal gas is neither for a small system with N particles nor at the thermodynamic limit extensive, so if strict extensivity for the entropy is requested the claim of statistical mechanics that the Boltzman entropy is a microscopic description of its thermodynamic analog is challenged.

Continuity of the entropy of macroscopic quantum systems.

- PhysicsPhysical 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 Gibbs paradox and the distinguishability of identical particles

- Physics
- 2010

Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the microlevel, and from the relation S=k ln W leads to a…

Thermodynamics of the System of Distinguishable Particles

- Physics, Computer ScienceEntropy
- 2009

The issue of the thermodynamics of a system of distinguishable particles is discussed and a straightforward way to get the corrected Boltzmann counting is shown, which can be justified in classical statistical mechanics.

Probability, Entropy, and Gibbs’ Paradox(es)

- PhysicsEntropy
- 2018

It is shown that contrary to what has often been suggested, quantum mechanics is not essential for resolving the paradoxes and includes the case of colloidal solutions, for which quantum Mechanics is not relevant.

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