Fluctuation theorems for autonomous work

Classical fluctuation theorems for work have been obtained theoretically, and verified experimentally, within a nonautonomous framework in which work is performed on a system of interest, S, by the external manipulation of a work parameter, such as a piston’s position. Here, we obtain fluctuation theorems within an autonomous framework in which S exchanges energy with a reversible work source, R. The two subsystems, R and S, interact with one another as they evolve under Hamiltonian or stochastic dynamics, without external intervention. In this setting, we must account for the backaction of S on R, which is absent in the nonautonomous setting. We obtain autonomous versions of standard fluctuation theorems for work and entropy production. In each case, we argue, the autonomous fluctuation theorem reduces to its nonautonomous counterpart when R’s inertia becomes infinitely large.