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We provide a Lyapunov convergence analysis for time-inhomogeneous variable coefficient stochastic differential equations (SDEs). Three typical examples include overdamped, irreversible drift, and underdamped Langevin dynamics. We first…

Probability · Mathematics 2024-02-05 Qi Feng , Xinzhe Zuo , Wuchen Li

The dynamics of probability density functions have been extensively studied in computational science and engineering to understand physical phenomena and facilitate algorithmic design. Of particular interest are dynamics formulated as…

Analysis of PDEs · Mathematics 2026-03-16 José A. Carrillo , Yifan Chen , Daniel Zhengyu Huang , Jiaoyang Huang , Dongyi Wei

The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the…

Strongly Correlated Electrons · Physics 2018-10-30 Marco Gabbrielli , Augusto Smerzi , Luca Pezzè

In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on…

Mathematical Physics · Physics 2013-01-18 J. -F. Bercher

Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…

Dynamical Systems · Mathematics 2025-10-09 Jason J. Bramburger , Giovanni Fantuzzi

Consider the centered Gaussian vector $X$ in $\R^n$ with covariance matrix $ \Sigma.$ Randomize $\Sigma$ such that $ \Sigma^{-1}$ has a Wishart distribution with shape parameter $p>(n-1)/2$ and mean $p\sigma.$ We compute the density…

Statistics Theory · Mathematics 2022-11-28 Gérard G. Letac

An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are…

Chaotic Dynamics · Physics 2021-06-22 Adam A. Sliwiak , Nisha Chandramoorthy , Qiqi Wang

Completely positive trace preserving maps are essential for the formulation of the second law of thermodynamics. The dynamics of quantum systems, correlated with their environments, are in general not described by such maps. We explore how…

Quantum Physics · Physics 2016-08-18 Sai Vinjanampathy , Kavan Modi

We investigate thermodynamic properties and instability conditions in intermediate energy heavy ion reactions. We define locally thermodynamic variables, i.e. density, pressure and temperature, directly from the phase space distribution of…

Nuclear Theory · Physics 2009-10-30 C. Fuchs , P. Essler , T. Gaitanos , H. H. Wolter

The quantum Fisher information matrix provides us with a tool to determine the precision, in any multiparametric estimation protocol, through quantum Cram\'er-Rao bound. In this work, we study simultaneous and individual estimation…

Quantum Physics · Physics 2019-04-17 L. Bakmou , A. Slaoui , M. Daoud , R. Ahl Laamara

In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.

General Mathematics · Mathematics 2010-11-11 Joakim Munkhammar

The data-driven characterization of the ``complexity'' present in dynamical systems remains an open problem with broad applications across the physical sciences. We investigate the ``structural complexity'' of the 2D ferromagnetic Ising…

Statistical Mechanics · Physics 2026-02-18 Cooper Jacobus

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…

Dynamical Systems · Mathematics 2019-08-17 Vieri Benci , Claudio Bonanno , Stefano Galatolo , Giulia Menconi , Federico Ponchio

In recent years, mutual information optimal control has been proposed as an extension of maximum entropy optimal control. Both approaches introduce regularization terms to render the policy stochastic, and it is important to theoretically…

Optimization and Control · Mathematics 2026-03-23 Shoju Enami , Kenji Kashima

We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…

Statistical Mechanics · Physics 2020-07-01 Sosuke Ito , Andreas Dechant

The thermodynamic uncertainty relation is an inequality stating that it is impossible to attain higher precision than the bound defined by entropy production. In statistical inference theory, information inequalities assert that it is…

Statistical Mechanics · Physics 2019-06-26 Yoshihiko Hasegawa , Tan Van Vu

Quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information will flow from the environments to…

Quantum Physics · Physics 2015-06-18 Xiang Hao , Ninghua Tong , Shiqun Zhu

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time…

chao-dyn · Physics 2016-08-31 R. Schack , C. M. Caves

With the help of the coherent states' basis we establish an interesting connection among i) the so-called Wehrl entropy, ii) Fisher's information measure $I$, and iii) the canonical ensemble entropy for the one-dimensional quantum harmonic…

Statistical Mechanics · Physics 2009-11-10 F. Pennini , A. Plastino

The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…

Quantum Physics · Physics 2018-03-30 Matthias M. Müller , Stefano Gherardini , Augusto Smerzi , Filippo Caruso