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The Gibbs Paradox.

Simon Saunders1

  • 1Faculty of Philosophy, University of Oxford, Oxford OX2 6GG, UK.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

The Gibbs Paradox is resolved by understanding particle indistinguishability in thermodynamics and statistical mechanics. This approach unifies classical and quantum theories by treating particle identity beyond simple labeling.

Keywords:
Gibbs paradoxclassicalentropy of mixingindistinguishabilityirreversibilitypermutation symmetryquantum

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Mechanics

Background:

  • The Gibbs Paradox highlights unresolved questions regarding the treatment of identical particles in thermodynamics and statistical mechanics.
  • Existing solutions are often limited to either classical or quantum theories, lacking a unified approach.

Purpose of the Study:

  • To provide a unified solution to the Gibbs Paradox applicable to both classical and quantum mechanics.
  • To re-evaluate the concept of particle distinguishability within thermodynamic and statistical frameworks.

Main Methods:

  • The study utilizes the concept of particle indistinguishability, extending Gibbs' notion of 'generic phase'.
  • It involves mathematical formulation at the tensor product of one-particle state spaces, leading to quotient spaces under permutations.
  • Eliminates sequence position as a particle labeling device.

Main Results:

  • A unified solution to the Gibbs Paradox is presented, bridging classical and quantum mechanics.
  • Particle indistinguishability is established as the core principle for resolving the paradox.
  • The concept of 'distinguishability' in classical statistical mechanics is identified as a convenient but physically inaccurate construct.

Conclusions:

  • The resolution of the Gibbs Paradox lies in correctly applying particle indistinguishability.
  • This approach offers a more rigorous and unified understanding of identical particles in physical systems.
  • It reframes 'distinguishability' as a useful mathematical tool rather than a fundamental physical property.