  We examine the Hall conductivity of macroscopic two-dimensional quantum
system, and show that the observed quantities can sometimes violate the
fluctuation dissipation theorem (FDT), even in the linear response (LR) regime
infinitesimally close to equilibrium. The violation can be an order of
magnitude larger than the Hall conductivity itself at low temperature and in
strong magnetic field, which are accessible in experiments. We further extend
the results to general systems and give a necessary condition for such
large-scale violation to happen. This violation is a genuine quantum phenomenon
that appears on a macroscopic scale. Our results are not only bound to the
development of the fundamental issues of nonequilibrium physics, but the idea
is also meaningful for practical applications, since the FDT is widely used for
the estimation of noises from the LRs.
