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For a system at given temperature, with energy known as a function of a setof variables, we obtain the thermal fluctuation of the evolution of thevariables by replacing the phase-space with a lattice and invoking theprinciple of detailed balance. Besides its simplicity, the asset of this methodis that it enables us to obtain the Langevin equation when the phase-space isanisotropic and when the system is described by means of curvilinearcoordinates. As an illustration, we apply our results to theKramer--Watts-Tobin equation in superconductivity. The choice between theIt\^{o} and the Stratonovich procedures is discussed.

Derivation of the Langevin equation from the principle of detailed balance