Dissipation: The phase-space perspective

We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by < W-diss >=< W >-Delta F=kTD(rho parallel to rho)=kT < ln(rho/rho)>, where rho and rho are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. D(rho parallel to rho) is the relative entropy of rho versus rho. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations.