The Dissipation Function: Its Relationship to Entropy Production, Theorems for Nonequilibrium Systems and Observations on Its Extrema

Abstract

In this chapter we introduce the dissipation function, and discuss the behaviour of its extrema. The dissipation function allows the reversibility of a nonequilibrium process to be quantified for systems arbitrarily close to or far from equilibrium. For a system out of equilibrium, the average dissipation over a period, t, will be positive. For field driven flow in the thermodynamic and small field limits, the dissipation function becomes proportional to the rate of entropy production from linear irreversible thermodynamics. It can therefore be considered as an entropy-like quantity that remains useful far from equilibrium and for relaxation processes. The dissipation function also appears in three important theorems in nonequilibrium statistical mechanics: the fluctuation theorem, the dissipation theorem and the relaxation theorem. In this chapter we introduce the dissipation function and the theorems, and show how they quantify the emergence of irreversible behaviour in perturbed, steady state, and relaxing nonequilibrium systems. We also examine the behaviour of the dissipation function in terms of the extrema of the function using numerical and analytical approaches.