Journal of Statistical Physics最新文献

Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 18 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure.

We establish a maximal large deviation principle for sequential dynamical systems with arbitrarily slow polynomial decay of correlations. We apply our result to a larger class of sequential interval maps, including Liverani-Saussol-Vaienti maps, intermittent maps with critical points, and Lasota-Yorke convex maps. We also recover several classical results on large deviations for these maps.

We consider (mathbb {Z}_q)-valued clock models on a regular tree, for general classes of ferromagnetic nearest neighbor interactions which have a discrete rotational symmetry. It has been proved recently that, at strong enough coupling, families of homogeneous Markov chain Gibbs states (mu _A) coexist whose single-site marginals concentrate on (Asubset mathbb {Z}_q), and which are not convex combinations of each other [1]. In this note, we aim at a description of the extremal decomposition of (mu _A) for (|A|ge 2) into all extremal Gibbs measures, which may be spatially inhomogeneous. First, we show that in regimes of very strong coupling, (mu _A) is not extremal. Moreover, (mu _A) possesses a single-site reconstruction property which holds for spin values sent from the origin to infinity, when these initial values are chosen from A. As our main result, we show that (mu _A) decomposes into uncountably many extremal inhomogeneous states. The proof is based on multi-site reconstruction which allows to derive concentration properties of branch overlaps. Our method is based on a new good site/bad site decomposition adapted to the A-localization property, together with a coarse graining argument in local state space.

The chemical master equation plays an important role in describing the time evolution of the probability of the number of reactants in a homogeneous chemical system. However, in complex systems, chemical reactions are often coupled with physical diffusion processes, which have a significant impact on the reaction dynamics, rendering the classical chemical master equation inadequate. Moreover, the reaction and diffusion processes are typically nonhomogeneous, further altering the time evolution of the chemical dynamic process. In this paper we propose a chemical continuous time random walks under anomalous diffusion model based on the renewal process where the waiting times are arbitrary distributed. By applying this model, we obtain the generalizations of the chemical diffusion master equation, the mass action laws, the fluctuation-dissipation theorem in the closed system, and the Gillespie algorithm to describe the effects of physical diffusion and the heterogeneity of the system. As an example, we analyze the monomolecular reaction-diffusion system with exponential and power-law waiting times, respectively, and show the fractional memory effect of the average of the concentrations of reactants on its history. This work gives one approach to describe anomalous diffusion with any reaction, and provides the systematic stochastic theory for modeling the heterogeneous chemical diffusive system.

This work is concerned with the large deviation principle (LDP) for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter (Hin (frac{1}{2},1)). We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply Khasminskii’s averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components. Finally, the moderate deviation principle (MDP) for the slow-fast systems is established based on the proof of the proposed LDP.

This note studies Hamiltonian systems which are thermostated using the Jellinek–Berry thermostat (J. Phys. Chem. 1988; Phys. Rev. A 1988). Jellinek & Jellinek and Berry propose an extension of Nosé’s thermostat (J. Chem. Phys. 1984). They introduce multiple functional parameters in order to achieve ergodicity of the thermostated dynamics. This family of Hamiltonian thermostats aims to simulate the canonical ensemble of a Hamiltonian H by coupling H to a 1-d heat reservoir with potential energy v(s) and kinetic energy (dfrac{1}{2Q}(p_s/u(s))^2). This note derives a normal form for the reservoir’s potential energy; investigates when the Jellinek–Berry thermostated system admits a Hoover reduction; and, demonstrates that a Jellinek–Berry thermostated periodic ideal gas is completely integrable and satisfies a KAM twist condition called Rüssmann non-degeneracy. This is used to deduce that a thermostated, collision-less, non-ideal gas (i.e. one with a smooth potential energy) at sufficiently high temperatures of the reservoir has a positive measure set of invariant tori–hence, the thermostated dynamics are non-ergodic.

It is well known that the mathematically accurate description of ordering and related symmetry breaking in statistical systems requires to consider the thermodynamic limit. But the order does not appear from nowhere, and yet before the thermodynamic limit is reached, there should exist some kind of preordering that appears and grows in the process of increasing the system size. The quantitative description of growing order, under the growing system size, is developed by introducing the notion of order indices. The rigorous proof of the phase transition existence is a separate difficult problem that is not the topic of the present paper. We illustrate the approach resorting to several models in the mean-field approximation, which makes it possible to demonstrate the notion of order indices for finite systems in a clear way. We show how the order grows on the way to the thermodynamic limit for Bose-Einstein condensation, arising superconductivity, magnetization, and crystallization phenomena.

We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles’ density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For appropriate choices of the boundary rates, these partial differential equations have more than one stationary solution. We prove the dynamical large deviations principle.

A modified noisy voter model is considered on time-varying scale-free networks with different degrees of assortativity. Within the model, the avalanche-like dynamics of the threshold variables (stress) assigned to voters leads to changes in their binary states (opinions). The system response to an avalanche is defined as the change in the system average opinion caused by this perturbation. It is shown analytically and numerically that increasing network assortativity leads to a disordering of the system dynamics. For systems of finite size, the dynamics changes from switching between consensuses to a state where opposing opinions coexist and the system average opinion is close to zero. At the same time, the increasing assortativity stabilizes the system response. This stabilization manifests itself in a decrease in both the maximum value of the response magnitude and the probability of large responses.

In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in [Ann. Phys. 377 (2017) 414–445] to the relativistic BGK model proposed by Marle. We present the perturbed Marle model around the generalized Jüttner distribution and investigate the properties of the linear operator. Then we prove the global existence and large-time behavior of classical solutions when the initial data is sufficiently close to a global equilibrium.