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1995

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/18824

Phenomenological approach to nonlinear Langevin equations

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http://dx.doi.org/10.1103/PhysRevE.52.5881

Abstract

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Subject

Equacions diferencials estocàstiques, Mecànica estadística, Equació de Fokker-Planck, Moviment brownià

Subject (English)

Stochastic differential equations, Statistical mechanics, Fokker-Planck equation, Brownian movements

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Articles publicats en revistes (Física de la Matèria Condensada)

Citation

BONET I AVALOS, Josep and PAGONABARRAGA MORA, Ignacio. Phenomenological approach to nonlinear Langevin equations. Physical Review E. 1995. Vol. 52, num. 6, pags. 5881-5892. ISSN 1063-651X. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/18824

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