Fisher Information Monotonicity along the Boltzmann and Landau Kinetic Equations
This concept covers how Fisher information - a convex functional measuring the smoothness or concentration of a probability density - behaves as a Lyapunov functional for kinetic equations. A learner sees that Fisher information decreases in time along the spatially homogeneous Boltzmann equation and along the Landau-Coulomb equation, why this monotonicity holds for all physically relevant interactions, and how it delivers regularity estimates for very singular (very soft) collision kernels via tools such as grazing-collision asymptotics, tensorisation, and Gamma calculus.
FISHER INFORMATION IN KINETIC THEORY C. VILLANI Abstract. These notes review the theory of Fisher
These are lecture notes by Cedric Villani reviewing Fisher information and its role in the kinetic theory of gases and plasmas. Fisher information is a convex functional of a probability density (ess…