  Based on the observation that the thermodynamic equilibrium free energy of an
open quantum system in contact with a thermal environment can be understood as
the difference between the free energy of the total system and that of the bare
environment, the validity of the Crooks theorem and of the Jarzynski equality
is extended to open quantum systems. No restrictions on the nature of the
environment or on the strength of the coupling between system and environment
need to be imposed. This free energy entering the Crooks theorem and the
Jarzynski equality is closely related to the Hamiltonian of mean force that
generalizes the classical statistical mechanical concept of the potential of
mean force.
