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arXiv · 0909.0579

Derivation of the Langevin equation from the principle of detailed balance

Jorge Berger
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Abstract

For a system at given temperature, with energy known as a function of a set of variables, we obtain the thermal fluctuation of the evolution of the variables by replacing the phase-space with a lattice and invoking the principle of detailed balance. Besides its simplicity, the asset of this method is that it enables us to obtain the Langevin equation when the phase-space is anisotropic and when the system is described by means of curvilinear coordinates. As an illustration, we apply our results to the Kramer--Watts-Tobin equation in superconductivity. The choice between the Itô and the Stratonovich procedures is discussed.

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Jorge Berger. 2010-06-03. Derivation of the Langevin equation from the principle of detailed balance. https://doi.org/10.1088/1742-5468%2F2010%2F07%2Fp07022

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