Abstract
The weak-noise limit of Fokker-Planck models is studied for the case where the steady-state probability density in that limit cannot be represented by a continuously differentiable nonequilibrium potential. In a previous paper [J. Stat. Phys. 35, 729 (1984)], we have shown that this corresponds to the general case in systems outside thermodynamic equilibrium. By using an extremum principle, the nondifferentiable potential is constructed, which generalizes the differentiable case. The relation of approximate differentiable potentials to the exact nondifferentiable potential is considered and discussed for two examples with attracting limit cycles, a periodically forced nonlinear oscillator, and two phase-coupled nonlinear oscillators. The relevance of nondifferentiable potentials for non- equilibrium thermodynamics is pointed out.
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