The Thermodynamic Dual Structure of Linear-Dissipative Driven Systems

It is often assumed that maximization of the statistical entropy cannot account for the spontaneous emergence of currents or compositional heterogeneity associated with them, and that other principles involving entropy production (its maximization or minimization) must be invoked to explain the emergence and robustness of the order in driven dissipative systems. I show for a class of simple models with driving and linear dissipation that the assumption is invalid. For dynamical ensembles, the exact entropy generally becomes a function of currents as well as the familiar equilibrium state variables, and from this richer dependence a full thermodynamic dual structure can be constructed, which predicts both emergence and robustness of nonequilibrium order. In systems of this type, the need for entropy production principles arises only if the exact entropy is replaced with a coarse-grained entropy function of the equilibrium state variables alone. I briefly consider some simple applications to thermal “ratchets,” in which induced cyclic currents display the essential elements of Onsager cycling in chemical reaction graphs.