Periodically driven jump processes conditioned on large deviations
Lydia Chabane, Raphaël Chétrite, Gatien Verley
Abstract
Abstract We study the fluctuations of systems modeled by time periodically driven Markov jump processes. We focus on observables defined through time-periodic functions of the system’s states or transitions. Using large deviation theory, canonical biasing and Doob transform, we characterize the asymptotic fluctuations of such observables after a large number of periods by obtaining the Markov process that produces them. We show that this process, called driven process, is the optimizer under constraint of the large deviation function for occupation and jumps.
Topics & Concepts
ObservableLarge deviations theoryStatistical physicsJumpRate functionMarkov processMathematicsFocus (optics)Constraint (computer-aided design)Markov chainFunction (biology)Jump processStochastic processPhysicsProbability density functionMathematical analysisProcess (computing)Time reversibilityMarkov propertyControl theory (sociology)Applied mathematicsStochastic processes and statistical mechanicsMathematical Dynamics and FractalsMarkov Chains and Monte Carlo Methods