  We study the entropy production in non-equilibrium quantum systems without
dissipation, which is generated exclusively by the spontaneous breaking of
time-reversal invariance. Systems which preserve the total energy and particle
number and are in contact with two heat reservoirs are analysed. Focussing on
point-like interactions, we derive the probability distribution induced by the
entropy production operator. We show that all its moments are positive in the
zero frequency limit. The analysis covers both Fermi and Bose statistics.
