When and why is the random force in Brownian motion a Gaussian process.
It is shown that the assumptions of causality and time-reversal invariance severely restrict the possibility to describe the fluctuations of a variable in a non-linear Markovian system using a Langevin equation. In fact a theorem is proven which implies that with the aforementioned assumptions a Langevin force which is independent of the state of the system is necessarily Gaussian and white. The theorem furthermore implies that such a description is only possible if the socalled "systematic force" is proportional to the derivative of the logarithm of the equilibrium distribution of the variable. Our analysis is given for a system with one variable which may be either even or odd under time reversal.
Mazur
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Instituut-Lorentz, University of Leiden, P.O. Box 9506, 2300 RA Leiden, the Netherlands.
Bedeaux
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