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.
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