On the Fermi-Dirac-type Fisher information

2025/08/20 by Zhu, Yuzhe
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.15054

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.

Citations

• The Landau equation does not blow up
• Nonlinear mobility continuity equations and generalized displacement convexity
• Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics
• Statistical mechanics of violent relaxation in stellar systems

Related

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