Possible canonical distributions for finite systems with nonadditive energy

TL;DR

This paper explores how finite systems in thermodynamic equilibrium with a small thermostat can exhibit q-exponential distributions due to energy nonextensivity, which revert to exponential in the thermodynamic limit.

Contribution

It demonstrates the conditions under which finite systems follow q-exponential distributions, emphasizing the importance of nonextensivity in small thermodynamic systems.

Findings

Finite systems can have q-exponential probability distributions.

Distribution approaches exponential form in the thermodynamic limit.

Nonextensivity significantly affects small system thermodynamics.

Abstract

It is shown that a small system in thermodynamic equilibrium with a finite thermostat can have a q-exponential probability distribution which closely depends on the energy nonextensivity and the particle number of the thermostat. The distribution function will reduce to the exponential one at the thermodynamic limit. However, the nonextensivity of the system should not be neglected.