[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.