Generalized diffusion and asymptotics induced by Tsallis entropy

TL;DR

This paper develops a generalized diffusion equation based on Tsallis entropy, compares its solutions with classical models, and explores their asymptotic behavior and mathematical properties.

Contribution

It introduces a novel diffusion model inspired by Tsallis entropy and analyzes its solutions and asymptotics, extending previous work on entropy-based diffusion processes.

Findings

Derived a new diffusion equation from Tsallis entropy principles.

Compared solutions with classical diffusion and porous medium equations.

Analyzed asymptotic behavior for large space and time variables.

Abstract

We formulate and solve the diffusion equation over a previously studied field $\mathcal{R}$, whose construction was motivated by the Tsallis entropy composition property. We compare this solution with the solutions of the diffusion and of the porous medium equations. We comment on the asymptotics of such solutions for large values of their spatial and temporal variables. We present conclusions for the generalised operations inspired by the Tsallis entropy composition and their relations to hyperbolicity.