Related papers: Thermalisation for Small Random Perturbations of D…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
We describe, at the microscopic level, the dynamics of N interacting components where the probability is very small when N is large that a given component interact more than once, directly or indirectly, up to time t, with any other…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
We investigate the asymptotic in $N$ of the mixing times of a Markov dynamics on $N-1$ ordered particles in an interval. This dynamics consists in resampling at independent Poisson times each particle according to a probability measure on…
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
Spontaneous symmetry breaking is a hallmark of equilibrium systems, typically characterized by a single critical point separating ordered and disordered phases. Recently, a novel class of non-equilibrium phase transitions was uncovered…
For the system with inhomogeneous distribution of macroscopic parameters we obtain thermodynamic relation which depends on the spatial point (coordinate). In our approach, to obtain such a relation we use the basic ideas of the method of…
In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…
Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a---possibly nonintegrable---reference dynamics, weakly perturbed…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We…
Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…
We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…
We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables,…
We investigate the thermalization dynamics of 1D systems with local constraints coupled to an infinite temperature bath at one boundary. The coupling to the bath eventually erases the effects of the constraints, causing the system to tend…
We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct…
Understanding how a system loses memory of its initial state is a central problem in probability and statistics. In this manuscript, we introduce the notion of abrupt decorrelation, which explicitly characterises a sharp and sudden loss of…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…