Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 11: Focus Session: Stochastic thermodynamics and information processing (joint session DY/BP)

DY 11.1: Hauptvortrag

Montag, 7. März 2016, 15:00–15:30, H44

Large deviation functionals in stochastic thermodynamics — •Andreas Engel, Johannes Hoppenau, and Daniel Nickelsen — Institut für Physik, Universität Oldenburg

The thermodynamic description of fluctuating systems is based on probability distributions for thermodynamic quantities like heat, work, and entropy. Unlike traditional statistical mechanics the tails of these distributions quantifying the frequency of rare, exceptional events are of particular interest. Large deviation theory is the proper mathematical framework to analyse these tails by introducing large deviation functions that characterize the probability of exponentially unlikely realizations.

A whole class of important large deviation functions deriving from a stationary stochastic process may be deduced from a single large deviation functional for its empirical density. For systems with detailed balance an explicit expression for this functional was derived in a series of mathematical papers by Donsker and Varadhan quite some time ago. We rederive their result using a path-integral approach and generalize it to non-equilibrium steady states. To this end the proper incorporation of the empirical probability current turns out to be crucial. We give explicit results for the large deviation functional, elucidate its connection with the entropy production and discuss the contraction to large deviation functions of more specific quantities.