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The Gibbs Paradox and Particle Individuality.

Dennis Dieks1

  • 1History and Philosophy of Science, Utrecht University, P. O. Box 85.170, 3508 AD Utrecht, The Netherlands.

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|December 3, 2020
PubMed
Summary

The Gibbs paradox in statistical physics, where mixing identical gases yields entropy, is resolved by orthodox statistical mechanics. This approach clarifies physical mechanisms and remains valid even in quantum mechanics.

Keywords:
Bose-EinsteinFermi-DiracGibbs paradoxdistinguishabilityidentical particles

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Area of Science:

  • Thermodynamics
  • Statistical Physics
  • Quantum Mechanics

Background:

  • The Gibbs paradox in classical thermodynamics is considered resolved, relating to entropy changes during gas mixing.
  • However, the Gibbs paradox persists in statistical physics, where standard calculations predict non-zero entropy for mixing identical gases, contradicting thermodynamic predictions.

Purpose of the Study:

  • To review the Gibbs paradox in statistical physics from an orthodox standpoint.
  • To demonstrate that standard statistical mechanics formalism can resolve this paradox.
  • To elucidate the physical mechanisms involved and its implications for quantum mechanics.

Main Methods:

  • Review of orthodox statistical mechanics formalism.
  • Analysis of the calculation of W (number of microstates) in entropy calculations.
  • Examination of the role of particle trajectories in classical statistical mechanics.
  • Discussion of the paradox's behavior in quantum mechanics.

Main Results:

  • The standard statistical mechanics formalism is capable of resolving the Gibbs paradox for identical gases.
  • Particle trajectories in the classical context offer intuitive physical explanations for the paradox.
  • The paradox's persistence in quantum mechanics, despite symmetrization postulates, is addressed.

Conclusions:

  • The Gibbs paradox in statistical physics is not a sign of fundamental flaws in S=klnW or its calculations.
  • Orthodox statistical mechanics provides a clear framework for understanding the physical mechanisms behind the paradox.
  • The paradox's resolution and implications extend to the quantum mechanical domain.