The Gibbs Paradox and Particle Individuality

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.