Stochastic simulations for the time evolution of systems which obey generalized statistics: Fractional exclusion statistics and Gentile's statistics

TL;DR

This paper introduces a stochastic simulation method for the time evolution of systems obeying generalized statistics, such as fractional exclusion and Gentile's statistics, enabling efficient modeling of interacting quantum systems out of equilibrium.

Contribution

The paper develops a novel stochastic approach for simulating non-equilibrium dynamics of systems with generalized statistics, derived within the canonical ensemble framework.

Findings

Analyzes thermodynamic differences between fractional exclusion and Gentile's statistics.

Demonstrates the method's efficiency in modeling interacting fermionic and bosonic systems.

Reveals key aspects related to species size in generalized statistical systems.

Abstract

We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of canonical ensembles. This approach introduces a tool for describing interacting fermionic and bosonic systems in non-equilibrium as ideal FES systems, in a computationally efficient manner. The two types of statistics are analyzed comparatively, indicating their intrinsic thermodynamic differences and revealing key aspects related to the species size.