Abstract
A dynamical system consisting of a subsystem having the variablesz=(q,p) and of another dynamical system (thermostat) is considered in the nonquantum case. Using a dynamical equation, it is shown that the linear and quadratic non-Markov fluctuation-dissipation relations (FDRs) of the first kind are valid in the first nonvanishing approximation in interaction constants. Applying these FDRs, one can determine the statistical properties of the fluctuations when the form of the nonlinear phenomenological equation is known. The non-Markov FDRs of the first kind are the direct generalization (to the inertial case) of the Markov FDRs that are the consequence of detailed balance.
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Stratonovich, R.L. Derivation of the linear and nonlinear non-Markov fluctuation-dissipation relations of the first kind for a dynamical model. J Stat Phys 53, 5–18 (1988). https://doi.org/10.1007/BF01011541
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DOI: https://doi.org/10.1007/BF01011541