Quantum entropy production as a measure of irreversibility
  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. 
I. Callens, W. De Roeck, T. Jacobs, C. Maes, K. Netocny