Unification of fluctuation theorems and one-shot statistical mechanics

Fluctuation-dissipation relations, such as Crooks’ Theorem and Jarzynski’s Equality, are powerful tools in quantum and classical nonequilibrium statistical mechanics. We link these relations to a newer approach known as “one-shot statistical mechanics.” Rooted in one-shot information theory, one-shot statistical mechanics concerns statements true of every implementation of a protocol, not only of averages. We show that two general models for work extraction in the presence of heat baths obey fluctuation relations and one-shot results. We demonstrate the usefulness of this bridge between frameworks in several ways. Using Crooks’ Theorem, we derive a bound on one-shot work quantities. These bounds are tighter, in certain parameter regimes, than a bound in the fluctuation literature and a bound in the one-shot literature. Our bounds withstand tests by numerical simulations of an information-theoretic Carnot engine. By analyzing data from DNA-hairpin experiments, we show that experiments used to test fluctuation theorems also test one-shot results. Additionally, we derive one-shot analogs of a known equality between a relative entropy and the average work dissipated as heat. Our unification of experimentally tested fluctuation relations with one-shot statistical mechanics is intended to bridge one-shot theory to applications. PACS numbers: 05.70.Ln, 05.40.-a, 03.67.-a 05.70.-a, a E-mail: [email protected] b E-mail: [email protected] 1 ar X iv :1 40 9. 38 78 v1 [ co nd -m at .s ta tm ec h] 1 2 Se p 20 14