Thermodynamic large fluctuations from uniformized dynamics

TL;DR

This paper introduces a uniformization technique to derive thermodynamic large deviation functions for continuous-time Markov processes from discrete-time Markov chains, enabling efficient simulation and analysis of nonequilibrium fluctuations.

Contribution

It presents a novel uniformization method that simplifies the calculation of large deviation functions and allows for efficient stochastic trajectory simulations in nonequilibrium thermodynamics.

Findings

Uniformization links continuous-time and discrete-time Markov processes for large deviations.

The method simplifies the computation of flux statistics in nonequilibrium systems.

Application to a stochastic pump model demonstrates the approach's effectiveness.

Abstract

Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we report that, using the technique of uniformization, the thermodynamic large deviation functions of continuous-time Markov processes can be obtained from Markov chains evolving in discrete time. This formulation offers new theoretical and numerical approaches to explore large deviation properties. In particular, the time evolution of autonomous and non-autonomous processes can be expressed in terms of a single Poisson rate. In this way the uniformization procedure leads to a simple and efficient way to simulate stochastic trajectories that reproduce the exact fluxes statistics. We illustrate the formalism for the current fluctuations in a stochastic pump model.