  We consider conservative quantum evolutions possibly interrupted by
macroscopic measurements. When started in a nonequilibrium state, the resulting
path-space measure is not time-reversal invariant and the weight of
time-reversal breaking equals the exponential of the entropy production. The
mean entropy production can then be expressed via a relative entropy on the
level of histories. This gives a partial extension of the result for classical
systems, that the entropy production is given by the source term of
time-reversal breaking in the path-space measure.
