  An isolated classical chaotic system, when driven by the slow change of
several parameters, responds with two reaction forces: geometric friction and
geometric magnetism. By using the theory of quantum fluctuation relations we
show that this holds true also for open quantum systems, and provide explicit
expressions for those forces in this case. This extends the concept of Berry
curvature to the realm of open quantum systems. We illustrate our findings by
calculating the geometric magnetism of a damped charged quantum harmonic
oscillator transported along a path in physical space in presence of a magnetic
field and a thermal environment. We find that in this case the geometric
magnetism is unaffected by the presence of the heat bath.
