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

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