Kappa Entropy and its Thermodynamic Connection

TL;DR

This paper introduces a new two-parameter nonadditive entropy linked to Kappa distributions, showing that thermodynamic laws hold only for a specific parameter value, thus connecting nonextensive entropy with thermodynamics.

Contribution

It proposes a novel two-parameter nonadditive entropy and establishes its thermodynamic consistency specifically at a certain parameter value, extending the understanding of Kappa-based statistical mechanics.

Findings

Thermodynamic laws are preserved only when a5=-5/2.

The new entropy is associated with a Kappa-type power-law velocity distribution.

The framework maintains thermodynamic consistency within a generalized power-law setting.

Abstract

Adopting a bottom-up perspective, we propose a novel two-parametric nonadditive entropy, $S_{\kappa\ell}$, associated with a Kappa-type power-law velocity distribution, $F_{\kappa\ell}(v)$, recently derived in the literature. By formulating an extended Neo-Boltzmannian microstate counting procedure and employing standard averaging techniques, we demonstrate that the fundamental laws of thermodynamics are preserved within this generalized power-law framework only whether $\ell=-5/2$, regardless of the values assumed by the $\kappa$-parameter.