Note on Boltzmann's H-Theorem and Detailed Balance Dynamics

Abstract: The Boltzmann H-theorem states that entropy of an ensemble of thermodynamic states increases until all states become equally probable. The evolution randomly picks one of the states in the ensemble and brings every other state to have the same probability as the selected state. Different realizations of evolution yield a distribution of selected states. We study this distribution numerically and discuss its relevance for equilibrium fluctuations in thermal as well as non thermal systems.