  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.

Statistical Mechanics;Quantum Physics