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By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…

Chaotic Dynamics · Physics 2007-05-23 Michael Blank

We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.

Dynamical Systems · Mathematics 2024-10-25 Sander C. Hille , Hanna Oppelmayer , Tomasz Szarek

Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…

Chaotic Dynamics · Physics 2015-06-15 Hidetoshi Aoki , Kunihiko Kaneko

Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…

Statistical Mechanics · Physics 2009-04-22 M. Süzen

Static granular packs have been studied in the last three decades in the frame of a modified equilibrium statistical mechanics that assumes ergodicity as a basic postulate. The canonical example on which this framework is tested consists in…

Soft Condensed Matter · Physics 2017-03-10 Paula A. Gago , Diego Maza , Luis A. Pugnaloni

We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…

Statistical Mechanics · Physics 2026-04-20 Vicenç Méndez , Carlos Hervás , Rosa Flaquer-Galmés

We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time--periodic force and a static bias. In doing so we focus on…

Statistical Mechanics · Physics 2023-06-21 Mateusz Wiśniewski , Jakub Spiechowicz

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

Optimization and Control · Mathematics 2022-06-01 Mohamed Maghenem , Elena Panteley , Antonio Loria

This paper presents an active search trajectory synthesis technique for autonomous mobile robots with nonlinear measurements and dynamics. The presented approach uses the ergodicity of a planned trajectory with respect to an expected…

Robotics · Computer Science 2017-08-31 Lauren M. Miller , Yonatan Silverman , Malcolm A. MacIver , Todd D. Murphey

We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…

Disordered Systems and Neural Networks · Physics 2009-11-13 Denis Boyer

We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to…

Statistical Mechanics · Physics 2007-05-23 Giulio Casati

We extend the notion of rational ergodicity to $\beta$-rational ergodicity for $\beta > 1$. Given $\beta \in \mathbb R$ such that $\beta > 1$, we construct an uncountable family of rank-one infinite measure preserving transformations that…

Dynamical Systems · Mathematics 2015-02-24 Terrence M. Adams , Cesar E. Silva

We study the vortex dynamics in an evolutive flow. We carry out the statistical analysis of the resulting time series by means of the joint use of a compression and an entropy diffusion method. This approach to complexity makes it possible…

Statistical Mechanics · Physics 2009-11-10 Jacopo Bellazzini , Giulia Menconi , Guido Buresti , Paolo Grigolini , Massimiliano Ignaccolo

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our…

Statistical Mechanics · Physics 2016-09-07 Dongliang Zhang , H. T. Quan , Biao Wu

We study the problem on the weak-star decomposability of a topological $\mathbb{N}_{0}$-dynamical system $(\Omega,\varphi)$, where $\varphi$ is an endomorphism of a metric compact set $\Omega$, into ergodic components in terms of the…

Dynamical Systems · Mathematics 2018-08-28 A. V. Romanov

We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…

Statistical Mechanics · Physics 2007-05-23 V. Benci , C. Bonanno , S. Galatolo , G. Menconi , M. Virgilio

We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations, we compute the structural properties of this model as a…

Statistical Mechanics · Physics 2015-12-31 K. Julian Schrenk , Daan Frenkel

We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…

Statistical Mechanics · Physics 2019-11-05 Denis S. Grebenkov

At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic…

Disordered Systems and Neural Networks · Physics 2018-02-14 Haijun Zhou , Kang Li

The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…

Statistical Mechanics · Physics 2026-03-10 M. Süzen