  For nonequilibrium steady states, we identify observables whose fluctuations
satisfy a general symmetry and for which a new reciprocity relation can be
shown. Unlike the situation in recently discussed fluctuation theorems, these
observables are time-reversal symmetric. That is essential for exploiting the
fluctuation symmetry beyond linear response theory. Besides time-reversal, a
crucial role is played by the reversal of the driving fields, that further
resolves the space-time action. In particular, the time-symmetric part in the
space-time action determines second order effects of the nonequilibrium
driving.
