Kappa Entropy and its Thermodynamic Connection

Abstract

Adopting a bottom-up perspective, we propose a novel two-parametric nonadditive entropy, $S_{\hat{I}º\ell }$, associated with a Kappa-type power-law velocity distribution, $F_{\hat{I}º\ell }(v)$, 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 $\hat{I}º$-parameter.

5 pages, 2 figures