Macroscopic Potentials of Dissipative Dynamical Systems

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The notion of a coarse grained thermodynamic potential is extended to non-equilibrium systems with stable, generally time dependent, steady states. A review is presented of recent results for this problem. The non-equilibrium potential is defined by an extremum principle incorporating the influence of weak noise, it satisfies a Hamilton Jacobi equation, which is generally non-integrable, and the potential is found, in general, to be continuous and single valued but only piecewise differentiable. Examples are studied exhibiting monostable and multistable behavior, including limit cycles.