A quantum solution to Gibbs Paradox with few particles

TL;DR

This paper provides a fully quantum mechanical analysis of the Gibbs paradox, demonstrating that entropy changes are identical for different particle types when using correct quantum states, and highlights the quantum origin of the paradox.

Contribution

It introduces a quantum solution to the Gibbs paradox using a gedanken experiment, clarifies the role of quantum statistics, and explores finite size effects on entropy change.

Findings

Entropy change is the same for bosons, fermions, and non-identical particles.

The initial state of identical particles is not a thermal equilibrium in conventional views.

Quantum mechanisms and finite size effects influence the entropy change during mixing.

Abstract

We present a fully quantum solution to the Gibbs paradox (GP) with an illustration based on a gedanken experiment with two particles trapped in an infinite potential well. The well is divided into two cells by a solid wall, which could be removed for mixing the particles. For the initial thermal state with correct two-particle wavefunction according to their quantum statistics, the exact calculations shows the entropy changes are the same for boson, fermion and non-identical particles. With the observation that the initial unmixed state of identical particles in the conventional presentations actually is not of a thermal equilibrium, our analysis reveals the quantum origin of the paradox, and confirm the E. J. Jaynes' observation that entropy increase in Gibbs mixing is only due to the including more observables measuring the entropy. To further show up the subtle role of the quantum mechanism in the GP, we study the different finite size effect on the entropy change and shows the works performed in the mixing process are different for various types of particle.