Integrating out the fast degrees of freedom in a quantum many-body system leaves us with an effective field theory of a (typically) non-equilibrium configuration of slow degrees of freedom. Using this EFT, a local form of the second law is derived: that in local equilibrium, the entropy production at each spacetime point is positive semidefinite. Interestingly, the analogue of the detailed balance condition seems to be the presence of a symmetry in the classical limit, in this case Z2, which defines an entropy current. The sign of the divergence of this current is determined by unitarity in the quantum theory.

The relation between unitarity violation and entropy generation is an interesting one, which is becoming increasingly well-understood via non-equilibrium formulations of QFT. It suggests that in future, we may be able to make sense of a unitarity breakdown (say at high energies) in terms of some non-adiabatic process.