Exact Stationary Solution of Fokker-Planck Equation and Generalized Potential for Non-Equilibrium Systems Without Detailed Balance |
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Authors: | Cun-Zheng NING Gang HU |
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Institution: | 1. Institut fuer Theoretische Physik und Synergetik, Universitaet Stuttgart, Pfaffenwaldring 5714, D-7000 Stuttgart 80, Germany;
2. Department of Physics, Beijing Normal University, Beijing 100875, China;
3. Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China |
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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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