Related papers: Information geometry of tempered stable processes

We use a database of direct numerical simulations to evaluate parametrizations for energy dissipation rate in stably stratified flows. We show that shear-based formulations are more appropriate for stable boundary layers than commonly used…

We investigate the thermalization of a stochastic system with discrete phase space, initially at equilibrium at temperature $T_i$ and then termalizing in an environment at temperature $T_f$ , considering both cases $T_i > T_f$ and $T_i <…

We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…

The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the…

We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…

(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…

We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…

In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The…

Irreversible processes accomplished in a fixed time involve nonlinearly coupled flows of matter, energy, and information. Here, using entropy production as an example, we show how thermodynamic uncertainty relations and speed limits on…

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…

A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…

Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…

We apply the adiabatic approximation to slow but finite-time thermodynamic processes and obtain the full counting statistics of work. The average work consists of change in free energy and the dissipated work, and we identify each term as a…

We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and…

We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order…

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…