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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Probability, Entropy, and Gibbs' Paradox(es).

Robert H Swendsen1

  • 1Physics Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

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

Physicists have debated Gibbs' paradox for over a century. This study resolves both classical paradoxes without quantum mechanics, even for colloidal solutions.

Keywords:
Gibbs’ paradoxentropystatistical mechanics

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Area of Science:

  • Thermodynamics and Statistical Mechanics
  • Physical Chemistry

Background:

  • Gibbs' paradox, concerning entropy in mixing systems, has puzzled physicists since the 1870s.
  • Existing resolutions often invoke quantum mechanics, despite the paradoxes being classical in origin.
  • The paradoxes are foundational to understanding statistical mechanics and thermodynamics.

Purpose of the Study:

  • To resolve the classical Gibbs' paradoxes without relying on quantum mechanics.
  • To provide a unified explanation applicable to both microscopic and macroscopic systems.
  • To demonstrate the irrelevance of quantum mechanics for certain classical systems like colloidal solutions.

Main Methods:

  • Analysis of classical thermodynamics and statistical mechanics principles.
  • Development of a resolution framework based on distinguishability and information.
  • Application of the framework to mixing processes, including ideal gases and colloidal systems.

Main Results:

  • A resolution to both Gibbs' paradoxes is presented, independent of quantum mechanics.
  • The framework successfully explains entropy changes in mixing ideal gases.
  • The resolution is shown to be valid for colloidal solutions, where quantum effects are negligible.

Conclusions:

  • Quantum mechanics is not a prerequisite for resolving Gibbs' paradox.
  • A classical approach provides a complete and sufficient explanation for the paradoxes.
  • The findings offer a deeper understanding of the foundations of statistical mechanics and thermodynamics.