THE LINEAR-RESPONSE APPROACH TO THE FOKKER-PLANCK EQUATION .1. THEORY

We show that a Brownian motion can be derived for a particle coupled t o a bath with a finite number of chaotic degrees of freedom, using no thermodynamics assumptions. We point out that although diffusion is ea sily derived in terms of the unperturbed bath via the central limit th eorem, friction is obtained only when the coupling between particle of interest and bath is considered. The only assumption made is that the bath should respond linearly (in statistical sense) to a weak externa l perturbation. We prove that the calculation of the friction can be t raced back to the bath susceptibility.