  We show that geometric phases may be generated in a quantum system subject to
noise by adiabatic manipulations of the fluctuating fields, e.g., by variation
of the system-environment coupling. For a two-state quantum system we express
this phase in terms of the geometry of the path, traversed by the slowly
varying direction and amplitude of the fluctuations. We discuss the origin of
this phase and possibilities to separate it from the known environment-induced
modification of the Berry phase.
