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Entropy production in random billiards and the second law of thermodynamics.

Banff International Research Station for Mathematical Innovation and Discovery

A random dynamical system is said to be time-reversible if the sta- tistical properties of orbits do not change after reversing the arrow of time. The degree of irreversibility is captured by the notion of en- tropy production rate. A general formula for entropy production will be presented that applies to a class of thermal perturbations of bil- liard systems, for which it is meaningful to talk about energy exchange between billiard particle and boundary. This formula establishes a re- lation between the purely mathematical concept of entropy production rate and the physical concept of thermodynamic entropy. In particular, it recovers Clausius formulation of the second law of thermodynamics: the system must evolve so as to transfer energy from hot to cold. Fur- ther connections with stochastic thermodynamics will be illustrated with examples of simple "billiard thermal engines." This is joint work with Tim Chumley.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Dynamical systems

video/mp4

Author affiliation: Washington University

2020-12-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76678

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/