Nonequilibrium potential for coexisting attractors

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Abstract
The weak-noise limit of Fokker-Planck models with coexisting attractors is analyzed and the nonequilibrium potential defined by the weak-noise limit of the probability density in the steady state is constructed. The nonequilibrium potential is found to be continuous with discontinuities in its first derivatives along certain surfaces in the configuration space, which are created by the coexistence of attractors. The general rules determining the position of these surfaces in configuration space are given. Numerical and approximate analytical results for the nonequilibrium potential of the Brownian motion in a periodic potential subject to an external force are obtained. A comparison with earlier work is presented.