A Dynamic Approach to the Thermodynamics of Superdiffusion

TL;DR

This paper proposes a dynamic framework linking thermodynamics and mechanics for superdiffusive systems with no finite time scale, by relating Tsallis entropy parameters to Levy index through dynamical methods.

Contribution

It introduces a novel dynamic approach connecting thermodynamics and mechanics in superdiffusive systems, expressing Tsallis entropic index as a function of Levy index.

Findings

Established a relation between Tsallis q and Levy alpha indices.

Provided a dynamical derivation linking thermodynamics to microscopic superdiffusive behavior.

Enhanced understanding of thermodynamics in systems with infinite time scales.

Abstract

We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Levy index alpha, and using dynamical rather than probabilistic arguments.