Statistical mechanical derivation of Jarzynski's identity for thermostated non-Hamiltonian dynamics

The recent Jarzynski identity (JI) relates thermodynamic free energy differences to nonequilibrium work averages. Several proofs of the JI have been provided on the thermodynamic level. They rely on assumptions such as equivalence of ensembles in the thermodynamic limit or weakly coupled infinite heat baths. However, the JI is widely applied to computer simulations involving finite numbers of particles, whose equations of motion are strongly coupled to a few extra degrees of freedom modeling a thermostat. In this case, the above assumptions are no longer valid. We propose a statistical mechanical approach to the JI solely based on the specific equations of motion, without any further assumption. We provide a detailed derivation for the non-Hamiltonian Nosé-Hoover dynamics, which is routinely used in computer simulations to produce canonical sampling.