On the Fermi-Dirac-type Fisher information
Analysis of PDEs
2025-08-22 v1 Mathematical Physics
math.MP
Abstract
We consider kinetic models for Fermi-Dirac-like particles obeying the exclusion principle. A generalized notion of Fisher information, tailored to kinetic equations of Fermi-Dirac-Fokker-Planck type, is introduced via the associated entropy dissipation identity. We show that, subject to a suitable upper bound on the initial data, this quantity decreases along solutions of the Fermi-Dirac-Fokker-Planck equation, while monotonicity can fail in the absence of such a bound. We also discuss the time evolution of this Fermi-Dirac-type Fisher information for the heat equation and the linear-type Landau-Fermi-Dirac equation with Maxwell molecules.
Keywords
Cite
@article{arxiv.2508.15054,
title = {On the Fermi-Dirac-type Fisher information},
author = {Yuzhe Zhu},
journal= {arXiv preprint arXiv:2508.15054},
year = {2025}
}