  Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS),
two pillars of statistical mechanics, are both broken in generic
driven-dissipative systems. These systems rather lead to non-equilibrium steady
states far from thermal equilibrium. Driven-dissipative Ising-type models,
however, are widely believed to exhibit effective thermal critical behavior
near their phase transitions. Contrary to this picture, we show that both the
FDR and TRS are broken even macroscopically at, or near, criticality. This is
shown by inspecting different observables, both even and odd operators under
time-reversal transformation, that overlap with the order parameter.
Remarkably, however, a modified form of the FDR as well as TRS still holds, but
with drastic consequences for the correlation and response functions as well as
the Onsager reciprocity relations. Finally, we find that, at criticality, TRS
remains broken even in the weakly-dissipative limit.
