On the Fermi-Dirac-type Fisher information

Yuzhe Zhu

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arXiv · 2508.15054

On the Fermi-Dirac-type Fisher information

Yuzhe Zhu

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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.

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Yuzhe Zhu. 2025-08-20. On the Fermi-Dirac-type Fisher information. https://arxiv.org/abs/2508.15054

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