The effects of coherence in quantum absorption refrigerators

Abstract

[eng] This work addresses the effect of coherence on different thermodynamic quantities of interest such as work or entropy production. Unlike other similar studies carried out previously, our work will also focus on the behavior of the fluctuations of the system which become of crucial importance at the quantum scale. To achieve this, the work is divided into three main blocks which are the theoretical background, the study of the stationary operation of the system and the optimization of the thermal machine performance. In chapters 2 and 3 we introduce open quantum systems and show that the Markovian dynamics of the system is well defined in terms of a master equation. From the master equation in Lindblad form we can obtain analytical expressions for the currents and their variances using the method of Full Counting Statistics, a formalism that we develop in detail. We also study the stochastic dynamics of the conditioned state of the system that allows us to calculate numerically the probability distributions associated with thermodynamic variables such as heat or entropy production, for which we present the formalism of the well-known quantum trajectories. Finally, we discuss the details of operation of our thermal machine, the quantum absorption refrigerator, and perform the microscopic derivation of the quantum master equation for this particular system, emphasizing each of the necessary approximations. In chapter 4 we proceed to solve the dynamics of the system focusing on its stationary regime, since this is the one in which the thermal machines operate. We study the relationship between coherence and heat flow, its fluctuations or entropy production. We also introduce a universal relation in classical Markovian jump processes out of equilibrium which is the Thermodynamic Uncertainty Relation andwe show that our system does not violate this relation. We also present a comparison between our coherent thermal machine and a similar incoherent machine. In chapter 5 we tackle the problem of optimizing the thermal machine. The novelties of our approach are the use of multi-objective optimization techniques that allow us to obtain many more solutions beyond the point of maximum power and also that we consider the possibility of not only maximizing the power and efficiency of the machine but we also take into account within the problem the minimization of fluctuations.