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Related papers: A note on Fisher Information hypocoercive decay fo…

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We prove that the reciprocal of Fisher information of a log-concave probability density $X$ in ${\bf{R}}^n$ is concave in $t$ with respect to the addition of a Gaussian noise $Z_t = N(0, tI_n)$. As a byproduct of this result we show that…

Information Theory · Computer Science 2015-06-23 G. Toscani

We show that to every small and decaying solution of the linearized constraint equations about Minkowski spacetime, one can add a quadratically small correction to obtain a solution of the full constraint equations. Near spacelike infinity,…

General Relativity and Quantum Cosmology · Physics 2026-03-25 Andrea Nützi

We explore the relationship between quantum Fisher information (QFI) and the negative of the second derivative of concurrence with respect to the coupling between two qubits, referred to as the curvature of entanglement (CoE). We analyze in…

Quantum Physics · Physics 2026-03-03 Zain H. Saleem , Anil Shaji , Anjala M Babu , Da-Wei Luo , Quinn Langfitt , Ting Yu , Stephen K. Gray

We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying ($1/r^\alpha$) interactions. We focus on two spin-$1/2$…

Disordered Systems and Neural Networks · Physics 2019-03-19 A. Safavi-Naini , M. L. Wall , O. L. Acevedo , A. M. Rey , R. M. Nandkishore

The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…

Methodology · Statistics 2023-06-06 William R. Coulton , Benjamin D. Wandelt

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…

Probability · Mathematics 2012-05-01 S. G. Bobkov , G. P. Chistyakov , F. Götze

The quadratic decaying property of the information rate function states that given a fixed conditional distribution $p_{\mathsf{Y}|\mathsf{X}}$, the mutual information between the (finite) discrete random variables $\mathsf{X}$ and…

Information Theory · Computer Science 2023-05-15 Michael X. Cao , Marco Tomamichel

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…

Quantum Physics · Physics 2011-12-08 Patrick J. Coles , Li Yu , Michael Zwolak

The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate…

Quantum Physics · Physics 2026-03-05 Tomohiro Nishiyama , Yoshihiko Hasegawa

We prove a bound on the entropy dissipation for the Boltzmann collision operator from below by a weighted $L^p$-Norm. The estimate holds for a wide range of potentials including soft potentials as well as very soft potentials. As an…

Analysis of PDEs · Mathematics 2022-12-20 Jamil Chaker , Luis Silvestre

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.…

Analysis of PDEs · Mathematics 2026-01-01 Nicolas Fournier , Stéphane Mischler

We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling…

Quantum Physics · Physics 2025-07-16 Hassan Manshouri , Moslem Zarei , Mehdi Abdi , Sougato Bose , Abolfazl Bayat

This paper extends the results regarding entropic convergence and the strong linearized limit for the Boltzmann equation (without external force) in [C. David Levermore. Entropic convergence and the linearized limit for the Boltzmann…

Analysis of PDEs · Mathematics 2025-10-07 Tina Mai

Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fisher information in the Boolean Central Limit Theorem and…

Probability · Mathematics 2026-03-02 Guillaume Cébron , Kewei Pan

This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain $\mathbb{T}^3$, using the…

Analysis of PDEs · Mathematics 2026-02-10 Yuhan Chen , Ning Jiang

We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial_t u=\ep \Delta u + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus, possibly, perturbations very small as $\Vert x…

Analysis of PDEs · Mathematics 2009-10-13 Matthieu Alfaro , Arnaud Ducrot

New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…

Information Theory · Computer Science 2024-05-07 Mokshay Madiman , Andrew Barron

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

Hypocoercivity methods are applied to linear kinetic equations without any space confinement, when local equilibria have a sub-exponential decay. By Nash type estimates, global rates of decay are obtained, which reflect the behavior of the…

Analysis of PDEs · Mathematics 2024-01-12 Emeric Bouin , Jean Dolbeault , Laurent Lafleche , Christian Schmeiser

We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole space $(x,v) \in…

Analysis of PDEs · Mathematics 2020-11-10 José A. Cañizo , Chuqi Cao , Josephine Evans , Havva Yoldaş