Irreversibility, Dissipation, and Its Measure: A New Perspective

Dissipation and irreversibility are two central concepts of classical thermodynamics that are often treated as synonymous. Dissipation D is lost or dissipated work Wdiss≥0 but is commonly quantified by entropy generation ΔiS in an isothermal irreversible macroscopic process that is often expressed as Kullback–Leibler distance DKL in modern literature. We argue that DKL is nonthermodynamic, and is erroneously justified for quantification by mistakenly equating exchange microwork ΔeWk with the system-intrinsic microwork ΔWk=ΔeWk+ΔiWk, which is a very common error permeating stochastic thermodynamics as was first pointed out several years ago, see text. Recently, it is discovered that dissipation D is properly identified by ΔiW≥0 for all spontaneously irreversible processes and all temperatures T, positive and negative in an isolated system. As T plays an important role in the quantification, dissipation allows for ΔiS≥0 for T>0, and ΔiS<0 for T<0, a surprising result. The connection of D with Wdiss and its extension to interacting systems have not been explored and is attempted here. It is found that D is not always proportional to ΔiS. The determination of D requires dipk, but we show that Fokker-Planck and master equations are not general enough to determine it, which is contrary to the common belief. We modify the Fokker-Planck equation to fix the issue. We find that detailed balance also allows for all microstates to remain disconnected without any transition among them in an equilibrium macrostate, another surprising result. We argue that Liouville’s theorem should not apply to irreversible processes, contrary to the claim otherwise. We suggest to use nonequilibrium statistical mechanics in extended space, where pk’s are uniquely determined to evaluate D.