Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems

R. Graham, T. Tél

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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.

Original languageEnglish
Pages (from-to)1109-1122
Number of pages14
JournalPhysical Review A
Volume31
Issue number2
DOIs
Publication statusPublished - 1985

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dynamical systems
oscillators
nonequilibrium thermodynamics
range (extremes)
thermodynamic equilibrium
cycles

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems. / Graham, R.; Tél, T.

In: Physical Review A, Vol. 31, No. 2, 1985, p. 1109-1122.

Research output: Contribution to journalArticle

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