A uniqueness-theorem for “linear” thermal baths Original Research Article

We consider systems in contact with a “linear” thermal bath, modeled by an additive thermal noise and an additive dissipation term which depends linearly on the system velocity. It is shown that the dissipation term and the bath temperature uniquely fix all statistical properties of the noise, without referring to any microscopic details of the bath. While the fluctuation dissipation theorem fixes only the second moment (correlation) of the noise, 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 noise statistics is always Gaussian.