### 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 language | English |
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Pages (from-to) | 1109-1122 |

Number of pages | 14 |

Journal | Physical Review A |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1985 |

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### 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.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 31, no. 2, pp. 1109-1122. https://doi.org/10.1103/PhysRevA.31.1109

}

TY - JOUR

T1 - Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems

AU - Graham, R.

AU - Tél, T.

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=18344391587&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18344391587&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.31.1109

DO - 10.1103/PhysRevA.31.1109

M3 - Article

AN - SCOPUS:18344391587

VL - 31

SP - 1109

EP - 1122

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -