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

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.

6 pages. Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment

References in corpus (4)

• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• H-theorem in quantum physics
• Entropy for Quantum Pure States and Its Dynamical Relaxation