Thermal Fluctuations in Nonlinear Systems

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Abstract
The simple physical assumptions on which the familiar linear fluctuation theory is based do not carry over to the nonlinear case. In order to treat this case, one has to start from the master equation, and expand it in reciprocal powers of a suitable parameter (roughly speaking, the size of the system). The successive powers yield first the phenomenological law, next the linear fluctuation theory, and subsequently the influence of nonlinearity in successive approximations. The coefficients in the expansion are connected with each other by relations of the same type as the fluctuation-dissipation theorem in the linear theory. Whether or not these relations are sufficient to uniquely determine the coefficients from phenomenological data is not known at present.

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