  The quantum statistical dynamics of a position coordinate x coupled to a
reservoir requires theoretically two copies of the position coordinate within
the reduced density matrix description. One coordinate moves forward in time
while the other coordinate moves backward in time. It is shown that quantum
dissipation induces, in the plane of the forward and backward motions, a
noncommutative geometry. The noncommutative geometric plane is a consequence of
a quantum dissipation induced phase interference which is closely analogous to
the Aharanov-Bohm effect.
