The generalized Langevin equation and the fluctuation- dissipation theorems

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Abstract
Two forms of Langevin equation are used to describe the equilibrium and nonequilibrium behaviour of a particle undergoing a Brownian motion. By comparing the results of these two forms it is shown that the fluctuation- dissipation theorems depend on two main assumptions. First, the after-effect functions are the same for the equilibrium and nonequilibrium states and second, the velocity power spectra are identical or the velocity autocorrelation function (V(t)V(t+T)) does not depend on the time t in the nonequilibrium state.

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