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We explore the concept of metastability in random dynamical systems, focussing on connections between random Perron-Frobenius operator cocycles and escape rates of random maps, and on topological entropy of random shifts of finite type. The…

Dynamical Systems · Mathematics 2012-09-13 Gary Froyland , Ognjen Stancevic

This article completes the study of the influence of the intensity parameter $\alpha$ in the boundary condition $\varepsilon \partial_{\boldsymbol{\nu}_\varepsilon} u_\varepsilon - u_\varepsilon \,…

Analysis of PDEs · Mathematics 2024-06-24 Taras Mel'nyk , Christian Rohde

We study asymmetric exclusion processes (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics (LK), that are…

Statistical Mechanics · Physics 2017-01-12 Bijoy Daga , Souvik Mondal , Anjan Kumar Chandra , Tirthankar Banerjee , Abhik Basu

The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant…

Chaotic Dynamics · Physics 2012-02-09 Gary P. Morriss

We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy for finite {M}arkov chains,'' J. Funct. Anal. 261(8), 2011)…

Optimization and Control · Mathematics 2026-04-09 Sawyer Robertson , Zhengchao Wan , Alexander Cloninger

We study the quantum Lyapunov exponent $\lambda_L$ in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of $N$ models coupled by disorder at large…

High Energy Physics - Theory · Physics 2022-08-31 Micha Berkooz , Adar Sharon , Navot Silberstein , Erez Y. Urbach

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…

Chaotic Dynamics · Physics 2018-03-14 Alexis Tantet , Valerio Lucarini , Henk A. Dijkstra

Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…

Statistical Mechanics · Physics 2019-03-12 Tsung-Cheng Lu , Tarun Grover

A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, a law of large numbers is shown to hold in a…

Probability · Mathematics 2021-11-10 D. A. Dawson , A. Sid-Ali , Y. Q. Zhao

We consider a family of Pomeau-Manneville type interval maps $T_\alpha$, parametrized by $\alpha \in (0,1)$, with the unique absolutely continuous invariant probability measures $\nu_\alpha$, and rate of correlations decay $n^{1-1/\alpha}$.…

Dynamical Systems · Mathematics 2016-04-28 Alexey Korepanov

The entanglement and localization in eigenstates of strongly chaotic subsystems are studied as a function of their interaction strength. Excellent measures for this purpose are the von-Neumann entropy, Havrda-Charv{\' a}t-Tsallis entropies,…

We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa}…

Chaotic Dynamics · Physics 2012-04-24 A. Y. Abul-Magd , M. Abdel-Mageed

This note shows how to considerably strengthen the usual mode of convergence of an $n$-particle system to its McKean-Vlasov limit, often known as propagation of chaos, when the volatility coefficient is nondegenerate and involves no…

Probability · Mathematics 2018-05-14 Daniel Lacker

The largest Lyapunov exponent of a system composed by a heavy impurity embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators is numerically computed for various values of the impurity mass $M$. A crossover between…

Chaotic Dynamics · Physics 2009-11-10 M. Romero-Bastida

In this paper we intend to present a unified treatment of a variety of singular interacting particle systems and their McKean-Vlasov limits. This unified approach is based on the use of the relative entropy on the path space in the spirit…

Analysis of PDEs · Mathematics 2024-12-11 Patrick Cattiaux

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…

Chaotic Dynamics · Physics 2011-07-13 A. S. de Wijn

We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the…

Probability · Mathematics 2025-11-06 Fan Chen , Zhenjie Ren , Songbo Wang

A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…

Statistical Mechanics · Physics 2010-08-18 B. N. Tiwari , Vinod Chandra , Subhashish Banerjee

In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular $L^p$-interactions as well as for the moderate interaction particle systems on the level of particle…

Probability · Mathematics 2022-06-17 Zimo Hao , Michael Röckner , Xicheng Zhang

Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to…

Statistical Mechanics · Physics 2011-01-04 Massmimo Coraddu , Marcello Lissia , Roberto Tonelli