Systems Far from Equilibrium

Abstract

In this chapter our focus will be on situations which are not close to thermal equilibrium. To understand the problems associated with it, we first discuss the situation close to equilibrium in a somewhat generalized setting. What we have repeatedly seen in the previous chapters is that small excursions from the equilibrium distribution relax to the equilibrium with time scales set by relaxation rates which we are familiar with in hydrodynamics-the mass or concentration diffusivity, the thermal diffusivity, momentum diffusivity. The balance between the fluctuating forces (obtained by averaging over small scale processes in the critical phenomena) and the dissipative processes ensured that the equilibrium distribution would be attained at t → ∞. Describing the system in terms of a fluctuating field ψ (→x), we have repeatedly used the free energy functional F(ψ)to describe the probability distribution e−F(ψ) for the weighting of the fluctuations and to describe the dynamics we have used a Langevin equation of the form

$$ \dot \psi = - \Gamma \frac{{\delta F}} {{\delta \psi }} + N $$

(6.1.1)