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-DeltaF=kTD(rho||rho[over ])=kT<ln(rho/rho[over ])>, where rho and rho[over ] 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||rho[over ]) is the relative entropy of rho versus rho[over ]. 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.
Kawai
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Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, USA.
Parrondo
J M R
JM
Van den Broeck
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