Thermodynamics with friction. I. The Clausius inequality revisited

Abstract

The different forms of the Clausius inequality are generalized to explicitly include frictional work, which can be partly dissipated as heat in the surroundings and thus contribute to increase its entropy so, in a cyclic process, the net entropy leaving the surroundings with the heat directly exchanged with the system is no longer constrained by the second law to be nonpositive. Likewise, the lower bound for the system’s entropy change in an arbitrary transformation is not now determined solely by the heat transferred from the surroundings but can be smaller by a term given by frictional dissipation in the latter. A wide range of applications is discussed, from thermal engines to mesoscopic devices, including the efficiency of dithermal engines and the problem of information erasure. Moreover, it is verified that the macroscopic approach utilized to extend standard macroscopic equilibrium theory in such a manner as to incorporate friction can be cast as well in the continuous, fieldlike formulation of nonequilibrium thermodynamics.