Macroscopic fluctuation theory

Stationary nonequilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several theoretical investigations, both analytic and numerical. The macroscopic fluctuation theory, based on a formula for the probability of joint space-time fluctuations of thermodynamic variables and currents, provides a unified macroscopic treatment of such states for driven diffusive systems. A detailed review of this theory including its main predictions and most relevant applications is given.

Figure 1

(a) Drawing of the unstable manifold. (b) Graph of the quasipotential. ${\rho }_c$ is a caustic point, e.g., $\mathcal{V}({\rho }_c,{\pi }_1)=\mathcal{V}({\rho }_c,{\pi }_3)$.

Figure 2

A caustic density profile for $E=\infty$. The shaded regions have equal area.