Related papers: Large deviation approach to nonequilibrium systems
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of…
We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…
We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…
Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…
Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
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…
We investigate the non-equilibrium large deviations function of the particle densities in two steady-state driven systems exchanging particles at a vanishing rate. We first derive through a systematic multi-scale analysis the coarse-grained…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.
We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium, nonequilibrium, and manmade stochastic systems. We give conditions for the convergence of…
We consider the long-term evolution of an inhomogeneous long-range interacting $N$-body system. Placing ourselves in the dynamically hot limit, i.e. neglecting collective effects, we derive a large deviation principle for the system's…
In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large…