Nonequilibrium work relations for systems subject to mechanical and thermal changes

Generalized forms of the Crooks fluctuation theorem are derived for non-Hamiltonian and Hamiltonian systems subject to both mechanical and thermal changes. Almost identical derivations are provided for the two cases under rather general assumptions. The basic one is that the probability distribution is a stationary solution of the Liouville equation for fixed values of mechanical control parameters applied to collective variables of the system and for fixed temperature. Generalized expressions for several nonequilibrium work relations derivable from the Crooks fluctuation theorem, such as the Jarzynski equality, path-ensemble averages for systems driven far from equilibrium, Bennett acceptance ratio, and two work-based potential of mean force estimators, are also derived. Although this list is not complete, the extension to other related work theorems is straightforward. The application of the methodology is illustrated for two representative cases, namely, for systems evolving with isochoric-isokinetic and isothermal-isobaric equations of motion.