相关论文: Metastability in Markov processes

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types…

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the…

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a non-equilibrium phase transition or a smooth but sharp…

We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of the order parameter to the ones of a…

By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic…

Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…

Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field…

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy…

We prove the metastable behavior of reversible Markov processes on finite state spaces under minimal conditions on the jump rates. To illustrate the result we deduce the metastable behavior of the Ising model with a small magnetic field at…

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size…

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…

In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how…

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…

We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…

We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…

The mechanism of appearance of exponentially large number of metastable states in magnetic phases of disordered Ising magnets with short-range random exchange is suggested. It is based on the assumption that transitions into inhomogeneous…

This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that…

This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…

We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous…

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…