Related papers: Fisher Information in Kinetic Theory
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann-Nordheim equations…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262…
In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…
The dynamics of relative entropy and $l_{1}$-norm of coherence, as well as, the Wigner-Yanase-skew and quantum Fisher information are studied for a time-dependent coupled XY spin chain in presence of a time-dependent transverse magnetic…
The paper deals with the reformulation of quantum uncertainty relation involving position and momentum of a particle on the basis of the Kerridge measure of inaccuracy and the Fisher information.
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
We investigate a symmetric logarithmic derivative (SLD) Fisher information for kinetic uncertainty relations (KURs) of open quantum systems described by the GKSL quantum master equation with and without the detailed balance condition. In a…
We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…
This paper gives an overview about particular quasi-entropies, generalized quantum covariances, quantum Fisher informations, skew-informations and their relations. The point is the dependence on operator monotone functions. It is proven…
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
In open quantum systems, we study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. With the time evolution, for the initial atom…
A possible thermalization of Fisher information is suggested for certain situations.
The net Fisher information measure, defined as the product of position and momentum Fisher information measures and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z=1-102, is found to correlate well with the…
A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information $\mathcal{I}_N$ in a Hamiltonian system of large particle number…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes…
We construct a smooth, strictly positive, Gaussian-decaying density on $\mathbb{R}^2$ for which Fisher information along the heat flow is not log-convex. This disproves the Cheng--Geng log-convexity conjecture in dimension two and, by…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…