Abstract
The weak-noise limit of Fokker-Planck models leads to a set of nonlinear Hamiltonian canonical equations. We show that the existence of a nonequilibrium potential in the weak-noise limit requires the existence of whiskered tori in the Hamiltonian system and, therefore, the complete integrability of the latter. A specific model is considered, where the Hamiltonian system in the weak-noise limit is not integrable. Two different perturbative solutions are constructed: the first solution describes analytically the breakdown of the whiskered tori due to the appearance of wild séparatrices; the second solution allows the analytic construction of an approximate nonequilibrium potential and an asymptotic expression for the probability density in the steady state.
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On leave from Institute for Theoretical Physics, Eötvös University, Budapest, Hungary.
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Graham, R., Tél, T. On the weak-noise limit of Fokker-Planck models. J Stat Phys 35, 729–748 (1984). https://doi.org/10.1007/BF01010830
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DOI: https://doi.org/10.1007/BF01010830