Derivation of the Langevin equation from the principle of detailed balance

Details Derivation of the Langevin equation from the principle of detailed balance Derivation of the Langevin equation from the principle of detailed balance

2009-09-03

arxiv.org/abs/0909.0579v2

J. Stat. Mech. (2010) P07022

Physics

Condensed Matter

Statistical Mechanics

minor changes

Scientific paper

10.1088/1742-5468/2010/07/P07022

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 It\^{o} and the Stratonovich procedures is discussed.

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