Canonical partition function for anomalous systems described by the $\kappa$-entropy

TL;DR

This paper derives the canonical $2$-partition function for systems described by $2$-entropy, enabling the calculation of macroscopic quantities and exploring the relationship with $2$-free energy.

Contribution

It introduces a novel expression for the canonical $2$-partition function based on the $2$-distribution, linking it to key thermodynamic quantities.

Findings

Derived the $2$-partition function from the $2$-distribution.

Expressed macroscopic quantities using the $2$-partition function.

Discussed the relationship between $2$-free energy and $2$-entropy.

Abstract

Starting from the $\kappa$-distribution function, obtained by applying the maximal entropy principle to the $\kappa$-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical $\kappa$-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the $\kappa$-partition function. The relationship between the associated $\kappa$-free energy and the $\kappa$-entropy is also discussed.