Generalized kinetic equations and effective thermodynamics

TL;DR

This paper introduces a new class of nonlocal kinetic and Fokker-Planck equations based on a generalized thermodynamics framework, capable of modeling phase transitions and blow-up phenomena across various physical and biological systems.

Contribution

It develops a novel nonlocal kinetic formalism linking diverse systems through long-range interactions, unifying concepts across physics, astrophysics, hydrodynamics, and biology.

Findings

Equations can describe phase transitions.

Framework captures blow-up phenomena.

Connects disparate systems via long-range interactions.

Abstract

We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can describe phase transitions and blow-up phenomena. On general grounds, our formalism can have applications in different domains of physics, astrophysics, hydrodynamics and biology. We find an aesthetic connexion between topics (stars, vortices, bacteries,...) which were previously disconnected. The common point between these systems is the (attractive) long-range nature of the interactions.