  We present a Gedankenexperiment that leads to a violation of detailed balance
if quantum mechanical transition probabilities are treated in the usual way by
applying Fermi's "golden rule". This Gedankenexperiment introduces a collection
of two-level systems that absorb and emit radiation randomly through
non-reciprocal coupling to a waveguide, as realized in specific chiral quantum
optical systems. The non-reciprocal coupling is modeled by a hermitean
Hamiltonian and is compatible with the time-reversal invariance of unitary
quantum dynamics. Surprisingly, the combination of non-reciprocity with
probabilistic radiation processes entails negative entropy production. Although
the considered system appears to fulfill all conditions for Markovian
stochastic dynamics, such a dynamics violates the Clausius inequality, a
formulation of the second law of thermodynamics. Several implications
concerning the interpretation of the quantum mechanical formalism are
discussed.
