Average Entropy Dissipation in Irreversible Mesoscopic Processes

The Clausius inequality is rectified to obtain expressions for the entropy produced as the result of irreversible work and/or heat exchanges. These are combined with the Jarzynski equality and its generalizations to explicitly relate mean (as opposed to transient) entropy dissipation to experimental or simulation observables. The results are extended to nonisothermal processes which begin and end at nonequilibrium steady states, leading to a new exact expression and positive lower bound for the resulting average entropy dissipation. The Carnot engine emerges as a limiting case of a family of irreversible processes arising from an interface between materials at different temperatures, whose mapping onto reversible and irreversible molecular extension experiments is discussed.

Figure 1

Schematic illustration of a nonisothermal irreversible cycle performed by moving a small (mesoscopic) piston $\chi (t)$ to vary the volume ($V$) and pressure ($P$) of a gas at temperature $T$, surrounded by another gas at a higher different temperature $T_0$. The solid points in the lower graph mark equilibrium states and the curves trace the instantaneous force per unit area experienced by the piston in representative nonequilibrium forward and reverse paths.