相关论文: Non equivalence of dynamical ensembles and emergen…
Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here we propose a theory of…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…
The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical applications. However, this property breaks down under…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
This paper tackles the issue of establishing a lower-bound on the asymptotic ratio of survival probabilities between two different initial conditions, asymptotically in time for a given Markov process with extinction. Such a comparison is a…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…
The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…
Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy of the two ensembles. In [3]…
We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second…
We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…
In this work, we study ergodicity of continuous time Markov processes on state space $\mathbb{R}_{\geq 0} := [0,\infty)$ obtained as unique strong solutions to stochastic equations with jumps. Our first main result establishes exponential…
We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…
A concept of emergence was recently introduced in the paper [Berger] in order to quantify the richness of possible statistical behaviors of orbits of a given dynamical system. In this paper, we develop this concept and provide several new…
The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically…
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these…