Microcanonical ensemble based on the superstatistics with the free Hamiltonian as a stochastic variable

Abstract

In this work, the general procedure for obtaining the superstatistical density of states, where the probability density function has the nonzero variance, is first developed. We then discuss the microcanonical ensemble based on the superstatistics with the free Hamiltonian as a stochastic variable. Finally, some applications of the formalism presented here are analyzed in detail within the framework of different probability distributions such as three states distribution, the Gamma distribution, the q-deformed Dirac delta distribution and the Poisson distribution.