  We theoretically study the geometric effect of quantum dynamical evolution in
the presence of a nonequilibrium noisy environment. We derive the expression of
the time dependent geometric phase in terms of the dynamical evolution and the
overlap between the time evolved state and initial state. It is shown that the
frequency shift induced by the environmental nonequilibrium feature plays a
crucial role in the geometric phase and evolution path of the quantum dynamics.
The nonequilibrium feature of the environment makes the length of evolution
path becomes longer and reduces the dynamical decoherence and non-Markovian
behavior in the quantum dynamics.
