Landauer's Principle in Repeated Interaction Systems

My masters thesis; essentially, an expanded version of most of arXiv:1510.00533, in my own words. The abstract: “Landauer’s Principle states that there is a lower bound on the energy required to change the state of a small system from an initial state to a final state by interacting with a thermodynamic reservoir; of particular interest is when the bound is saturated and the minimal energy cost obtained for a given state transformation. We investigate Landauer’s Principle in the context of repeated interaction systems (RIS), a class of physical systems in which a small system of interest interacts with a sequence of thermal probes. In particular, we show that for RIS, Lan- dauer’s bound is not saturated generically in the adiabatic limit, in which time evolution can be thought of as proceeding infinitely slowly, in contrast to the case of the interaction of a system and a single thermodynamic reservoir. However, for a specific RIS which models the small sys- tem and the probes as 2-level systems interacting via a dipole interaction in the rotating wave approximation, Landauer’s bound is saturated adiabatically. In this work, we also formulate and prove a discrete non-unitary adiabatic theorem to use for RIS.