Onsager reciprocal relations with broken time-reversal symmetry

We provide analytical and numerical evidence that Onsager reciprocal relations remain valid for systems with broken time-reversal symmetry as is typically the case when a generic magnetic field is present. Our results show that the Onsager reciprocal relations are much more general than previously assumed. Hence, the fundamental constraints they impose on heat to work conversion remain valid also with broken time-reversal symmetry. In particular, the possibility of an engine operating at the Carnot efficiency with finite power is ruled out on purely thermodynamic grounds.