Canonical equilibrium distribution derived from Helmholtz potential

TL;DR

This paper offers a new derivation of the canonical equilibrium distribution based on Helmholtz free energy, applicable to all trace-form entropies, and demonstrates that Tsallis entropy results in inverse power law distributions.

Contribution

It introduces an alternative derivation method for the canonical distribution using Helmholtz free energy, applicable to all trace-form entropies, including Tsallis entropy.

Findings

Derivation based on Helmholtz free energy is valid for all trace-form entropies.

Tsallis entropy produces genuine inverse power law distributions.

The approach provides a thermodynamic foundation for generalized entropies.

Abstract

Plastino and Curado [Phys. Rev. E 72, 047103 (2005)] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy showing that the Tsallis entropy yields genuine inverse power laws.