According
to the second law, the work needed to bring a system from one
state to another one, when in contact with a heat bath, is at least
equal to the difference in free energies of these states. By a
refinement of the Crooks equality, we derive an exact microscopic
expression for the extra dissipation. It is expressed in terms of the
relative entropy of the phase space density. Furthermore, lower bounds
for the extra dissipation are obtained when only limited information is
available. The result is illustrated on various Hamiltonian and
stochastic models. The connection to the thermodynamics of computation
is discussed.
Ref:
Kawai, Parrondo and Van den Broeck, Phys
Rev Lett
98, 080602 (2007).