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In this paper we present a self-contained macroscopic description ofdiffusive systems interacting with boundary reservoirs and under the action ofexternal fields. The approach is based on simple postulates which are suggestedby a wide class of microscopic stochastic models where they are satisfied. Thedescription however does not refer in any way to an underlying microscopicdynamics: the only input required are transport coefficients as functions ofthermodynamic variables, which are experimentally accessible. The basicpostulates are local equilibrium which allows a hydrodynamic description of theevolution, the Einstein relation among the transport coefficients, and avariational principle defining the out of equilibrium free energy. Associatedto the variational principle there is a Hamilton-Jacobi equation satisfied bythe free energy, very useful for concrete calculations. Correlations over amacroscopic scale are, in our scheme, a generic property of nonequilibriumstates. Correlation functions of any order can be calculated from the freeenergy functional which is generically a non local functional of thermodynamicvariables. Special attention is given to the notion of equilibrium state fromthe standpoint of nonequilibrium.

Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems