相关论文: Fisher information for solutions of the Boltzmann …

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.…

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--Coulomb equation is put in perspective and generalised.…

In this note we prove that, under some minimal regularity assumptions on the initial datum, solutions to the spatially homogenous Boltzmann and Landau equations for hard potentials uniformly propagate the Fisher information. The proof of…

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…

We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality (Cie\'slak--Fuest--Hajduk--Sier\.z\k{e}ga, 2024),…

This note deals with the linear Boltzmann equation in the non-compact setting with a confining potential which is close to quadratic. We prove that in this case, starting from a smooth initial datum, the Fisher Information (hence, the…

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 show that the nonlocal Fisher information - defined as the entropy dissipation of the Boltzmann entropy for nonlocal heat equations - admits a natural lifting in the sense of Guillen and Silvestre (2025). Important examples include the…

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 prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…

Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…

We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…

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…

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…

We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately soft potentials, $\gamma \in (-2,0)$ with the common notation.…

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 quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…

In this study, we model the dark matter and baryon matter distribution in the Cosmic Web by means of highly nonlinear Schr\"{o}dinger type and reaction diffusion wave mechanical descriptions. The construction of these wave mechanical models…

We present a pointwise inequality for adjacent even Legendre polynomials in high dimensional spheres featuring the effect of spectral gaps. This improves a recent result of Imbert, Silvestre and Villani that is crucially used in their study…

In this work we consider a Fisher-Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry reductions in partial differential equations. Through…