Equilibration by quantum observation

We consider an unexplored regime of open quantum systems that relax via coupling to a bath while being monitored by an energy meter. We show that any such system inevitably reaches an equilibrium (quasi-steady) state controllable by the effective rate of monitoring. In the non-Markovian regime, this approach suggests the possible 'freezing' of states, by choosing monitoring rates that set a non-thermal equilibrium state to be the desired one. For measurement rates high enough to cause the quantum Zeno effect, the only steady state is the fully mixed state, due to the breakdown of the rotating wave approximation. Regardless of the monitoring rate, all the quasi-steady states of an observed open quantum system live only as long as the Born approximation holds, namely the bath entropy does not change. Otherwise, both the system and the bath converge to their fully mixed states.