Related papers: Fisher Information in Kinetic Theory
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 classical interactions derived from systems of particles.…
We establish an a priori estimate for the dissipation of the Fisher information for the space-homogeneous Landau equation with very soft potentials. This work is motivated by the recent breakthrough by Guillen and Silvestre, which proves…
We study a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for moderately soft potentials. The spatial delocalization introduced in the collision operator not only…
This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This classical functional from information theory is shown to be…
We consider the Fisher information for spatially homogeneous multi-species Landau system. We show that the mass-weighted Fisher information is monotone decreasing in time along the solutions of the Landau system with a general class of…
A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…
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…
We consider the Kac model for the space-homogeneous Landau equation with the Coulomb potential. We show that the Fisher information of the Liouville equation for the unmodified $N$-particle system is monotonically decreasing in time. The…
The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…
The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
We consider the Landau-Coulomb equation for initial data with bounded mass, finite numbers of moments, and entropy. We show the existence of a global weak solution that has bounded Fisher information for positive times. This solution is…
In this paper, we study the GENERIC structures of multi-species spatially inhomogeneous Boltzmann and Landau equations with Bose-Einstein, Maxwell-Boltzmann, and Fermi-Dirac statistics. In addition, under suitable assumptions on the…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
We consider the spatially homogeneous Landau equation for multiple species with different masses. As in the single-species case, the singularity of the collision operator is determined by a parameter $\gamma \in [-3,1]$, where $\gamma = -3$…
We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials…
A simple proof is given for the monotonicity of entropy and Fisher information associated to sums of i.i.d. random variables. The proof relies on a characterization of maximal correlation for partial sums due to Dembo, Kagan and Shepp.
We study the properties of optical pulse in cubic-quintic nonlinear media using information theoretic approach. The system can support regular (sharp top) and flat top pulse depending on the type of quintic interaction and the frequency of…
We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization…
The goal of this work is to introduce and investigate a generalised Fisher Information in the setting of linear Fokker-Planck equations. This functional, which depends on two functions instead of one, exhibits the same decay behaviour as…