Generalized Entropy Approach for Conserved Systems with Finite Entities: Insights into Non-Gaussian and Non-Chi-Square Distributions using Havrda-Charvat-Tsallis Entropy

Abstract

We demonstrate that the most probable state of a conserved system with a limited number of entities or molecules is the state where non-Gaussian and non-chi-square distributions govern. We have conducted a thought experiment using a specific setup. We have verified the mathematical derivation of the most probable state accurately predicts the results obtained by computer simulations. The derived distributions approach the Gaussian and the chi-square distributions as the number of entities approaches infinity.