The Gibbs Paradox and the Distinguishability of Identical Particles

Abstract

Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and from the relation S = k ln W leads to a non-extensive expression for the entropy. This result is usually considered incorrect because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency that identical particles are fundamentally indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In contrast, we argue that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly acceptable from both a theoretical and an experimental perspective. The inconsistency with thermodynamics can be removed by taking into account that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. We observe that even identical quantum particles are in some cases distinguishable, and conclude that quantum mechanics is irrelevant to the Gibbs paradox.

15 pages

References in corpus (3)

• How Classical Particles Emerge From the Quantum World
• Identical Quantum Particles and Weak Discernibility
• Thermodynamics of the System of Distinguishable Particles

Cited by in corpus (15)

• Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models
• The Gibbs Paradox
• The definition of the thermodynamic entropy in statistical mechanics
• The Logic of Identity: Distinguishability and Indistinguishability in Classical and Quantum Physics
• Statistical mechanics of self-gravitating systems: mixing as a criterion for indistinguishability
• Mixing indistinguishable systems leads to a quantum Gibbs paradox
• The Peculiar Status of the Second Law of Thermodynamics and the Quest for its Violation
• Demonstration and resolution of the Gibbs paradox of the first kind
• Plea for the use of the exact Stirling formula in statistical mechanics
• Ensemble equivalence for distinguishable particles
• The Gibbs Paradox and the Physical Criteria for the Indistinguishability of Identical Particles
• Active sorting of particles as an illustration of the Gibbs mixing paradox
• Clausius vs. Boltzmann-Gibbs entropies
• Is There a Unique Physical Entropy? Micro versus Macro
• Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior