A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution

We present a derivation of the Jarzynski identity and the Crooks fluctuation theorem for systems governed by deterministic dynamics that conserves the canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics, Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a relation between the heat absorbed by the system during the non-equilibrium process and the Jacobian of the phase flow generated by the dynamics.