  We show that in driven systems the Gaussian nature of the fluctuating force
and time-reversibility are equivalent properties. This result together with the
potential condition of the external force drastically restricts the form of the
probability distribution function, which can be shown to satisfy
time-independent relations. We have corroborated this feature by explicitly
analyzing a model for the stretching of a polymer and a model for a suspension
of non-interacting Brownian particles in steady flow.
