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math.AP2025
Fisher Information in Kinetic Theory
Cédric Villani
These notes review the theory of Fisher information, especially its use in kinetic theory of gases and plasmas. The recent monotonicity theorem by Guillen--Silvestre for the Landau…
math.AP2024
On the monotonicity of the Fisher information for the Boltzmann equation
Cyril Imbert, Luis Silvestre, Cédric Villani
We prove that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all…
math.AP2007★ 3 cited
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
I. M. Gamba, V. Panferov, C. Villani
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution,…