Multi-species kinetic models: GENERIC formulation and Fisher information

TL;DR

This paper explores the GENERIC framework for multi-species kinetic equations with different quantum statistics and demonstrates that Fisher information decreases over time in certain cases, providing insights into their thermodynamic properties.

Contribution

It introduces a GENERIC formulation for multi-species kinetic models with quantum statistics and proves Fisher information decay under specific conditions.

Findings

Fisher information is non-increasing in time for the multi-species Boltzmann equation.

The paper establishes the GENERIC structure for multi-species kinetic equations.

Analysis includes Bose-Einstein, Maxwell-Boltzmann, and Fermi-Dirac statistics.

Abstract

In this paper, we study the GENERIC structures of multi-species spatially inhomogeneous Boltzmann and Landau equations with Bose-Einstein, Maxwell-Boltzmann, and Fermi-Dirac statistics. In addition, under suitable assumptions on the collision kernels, we show that the Fisher information for the multi-species spatially homogeneous Boltzmann equation is non-increasing in time.