Related papers: Large Deviations of Irreversible Processes

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present…

We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…

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…

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…

Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…

In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…

In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of…

Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of…

We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…

The meaning of thermodynamic descriptions is found in large-deviations scaling of the fluctuations probabilities. The primary large-deviations rate function is the entropy, which is the basis for both fluctuation theorems and for…

This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…

We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where…

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an…

To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…

This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…

We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…