Two approaches to small-scale and quantum thermodynamics are fluctuation
relations and one-shot statistical mechanics. Fluctuation relations (such as
Crooks' Theorem and Jarzynski's Equality) relate nonequilibrium behaviors to
equilibrium quantities such as free energy. One-shot statistical mechanics
involves statements about every run of an experiment, not just about averages
over trials.
We investigate the relation between the two approaches. We show that both
approaches feature the same notions of work and the same notions of probability
distributions over possible work values. The two approaches are alternative
toolkits with which to analyze these distributions. To combine the toolkits, we
show how one-shot work quantities can be defined and bounded in contexts
governed by Crooks' Theorem. These bounds provide a new bridge from one-shot
theory to experiments originally designed for testing fluctuation theorems.Comment: 37 pages, 6 figure
