Non-Equilibrium Thermodynamics

Non-equilibrium thermodynamics is the study of thermodynamic systems that are not in thermodynamic equilibrium, where macroscopic flows of matter and energy drive the system into states that cannot be described by equilibrium statistical mechanics alone. The field was developed primarily by Ilya Prigogine and his Brussels school, who showed that far from equilibrium, systems can spontaneously develop ordered structures — dissipative structures — that export entropy to their surroundings.

Unlike equilibrium thermodynamics, where the state of a system is fully specified by a few macroscopic variables, non-equilibrium thermodynamics must account for flows, gradients, and the rates of entropy production. The linear regime near equilibrium is described by the Onsager reciprocal relations, but the truly interesting phenomena — bifurcations, pattern formation, self-organization — occur in the nonlinear, far-from-equilibrium regime where no universal variational principle is known to hold.

The field has experienced a renaissance through stochastic thermodynamics, which extends thermodynamic concepts to individual trajectories and small systems, and through the discovery of fluctuation theorems that generalize the second law to arbitrary non-equilibrium processes.