Proof of quantum mechanical H-theorem beyond binary collisions in quantum gases

TL;DR

This paper proves the quantum mechanical H-theorem for dilute Bose and Fermi gases by extending the quantum Boltzmann equation to include all many-body elastic collisions, enhancing understanding of thermodynamics in quantum gases.

Contribution

It generalizes the quantum H-theorem to include all many-body elastic collisions, beyond previous binary collision limitations, within the Lippmann-Schwinger formalism.

Findings

Proved the quantum H-theorem for dilute quantum gases.

Extended the quantum Boltzmann equation to many-body collisions.

Provides insights into the second law of thermodynamics for quantum systems.

Abstract

We have proved the quantum mechanical H-theorem for dilute Bose and Fermi gases by generalizing the quantum statistical Boltzmann equation for all possible many-body elastic collisions among the particles in the quantum gases within the Lippmann-Schwinger formalism. Previous study by Pauli did almost the same only for binary elastic collisions. We are considering all possible many-body elastic collisions for the current study. Our proof offers a better understanding to the foundation of the second law of thermodynamics for quantum gases.