A uniqueness-theorem for "linear" thermal baths

We consider systems in contact with a "linear" thermal bath, modeled by an additive thermal noise and an additive dissipation term which depends linea rly on the system velocity. It is shown that the dissipation term and the b ath temperature uniquely fix all statistical properties of the noise, witho ut referring ito any microscopic details of the bath. While the fluctuation dissipation theorem fixes only the second moment (correlation) of the nois e, our present theorem extends to all moments. As a consequence, any linear thermal bath can be imitated by a harmonic oscillator bath model and the n oise statistics is always Gaussian. (C) 2001 Elsevier Science B.V. All righ ts reserved.