Exact Stationary Solution of Fokker-Planck Equation and Generalized Potential for Non-Equilibrium Systems Without Detailed Balance

Cun-Zheng NING, Gang HU

Communications in Theoretical Physics ›› 1991, Vol. 16 ›› Issue (4) : 415-420.

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Communications in Theoretical Physics ›› 1991, Vol. 16 ›› Issue (4) : 415-420.
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Exact Stationary Solution of Fokker-Planck Equation and Generalized Potential for Non-Equilibrium Systems Without Detailed Balance

  • Cun-Zheng NING1, Gang HU2,3
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Abstract

An exact analogy is approached between systems in thermal equilibrium and those far from equilibrium which can be the cases without detailed balance. The analogy is based on the requirement that a given drift in the Fokker-Planck equation can be decomposed into two parts, one of which is divergence-free and the other can be derived from a potential which is invariant along the direction of the first part. If the conditions are fulfilled the Fokker-Planck equation changes in to a standard Poisson equation. The relations of this requirement to other conditions are diecussed. As a concrete example, the stationary Fokker-Planck equation for optical bistability is solved by using"this method.

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Cun-Zheng NING, Gang HU. Exact Stationary Solution of Fokker-Planck Equation and Generalized Potential for Non-Equilibrium Systems Without Detailed Balance[J]. Communications in Theoretical Physics, 1991, 16(4): 415-420

References

[1] R. Graham and H. Haken, Z. Phys. 245(1971)289; 245(1971)141.

[2] R. Graham and A. Schenzle, Phys. Rev. A25(1981)1302.

[3] Qiang ZHENG and Bai-Lin HAO, Commun. Theor. Phys. 8(1987)153.

[4] 1.1. Fedchenia, Ptyeica, 123A(1984)535.
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