Zeno Thermodynamics - Using the quantum Zeno effect to control heat machines driven by the smallest thermal baths

How small can a thermal bath be? Can the smallest baths properly drive microscopic heat machines? A closed small quantum system that includes both the machine and the baths will have recurrences and oscillate in time between engine and refrigerator operation. We show that these oscillations can be eliminated by inducing a partial Zeno effect via external dephasing of the baths. The machine keeps operating as a quantum heat machine until a global steady state is achieved with zero energy flows. Experimentally, dephasing is often easy to implement, and therefore it can be considered as a "free operation". We show analytically that in the limit of strong dephasing the dynamics of a system connected to a Zeno bath is Markovian - regardless of how small the bath is. In addition, we derived a simple reduced equation that accurately describes the non-Markovian dynamics in short evolution time or when the dephasing is weak. When starting out of equilibrium the Zeno bath monotonically relaxes to a generalized Gibbs state that maximizes the entropy under the constraints of the relevant conservation laws. These generalized Gibbs states contain information on classical correlations inside the bath. Despite the role of this correlation in entropy dynamics, we show that Carnot theorem and the standard second law still hold without any alteration. Present technology seems to be sufficient for the construction of such baths in various physical systems. Zeno baths can be used as a fundamental building block in experiments in quantum thermodynamics and stochastic thermodynamics. In addition, these baths give rise to new theoretical questions and challenges.