Thermodynamics and synchronization in open quantum systems

Dissipation effects have profound consequences in the behavior and properties of quantum systems. The unavoidable interaction with the surrounding environment, with whom systems continuously exchange information, energy, angular momentum or matter, is ultimately responsible of decoherence phenomena and the emergence of classical behavior. However, there exist a wide intermediate regime in which the interplay between dissipative and quantum effects gives rise to a plethora of rich and striking phenomena that has only started to be understood. In addition, the recent breakthrough techniques in controlling and manipulating quantum systems in the laboratory has made this phenomenology accessible in experiments and potentially applicable. In this thesis we aim to explore from a theoretical point of view some of the connections between dissipative and quantum effects. We focus on three main topics: the relation between dynamical and quantum correlations, the thermodynamical properties of fluctuations, and the performance of quantum thermal machines.

First, we study the emergence of transient and asymptotic spontaneous synchronization induced by dissipation in harmonic quantum systems and its connections with quantum correlations. Our results show that synchronization may be used a witnesses for the slow decay or even the preservation of quantum discord in many situations of interest. Furthermore, we develop methods for engineering it in complex harmonic networks or selected clusters, where noiseless subsystems can be obtained by tuning one or few system parameters.

Second, we explore the quantum versions of work and entropy production fluctuation relations. We derive a general fluctuation theorem valid for a broad class of open systems dynamics and discuss the meaning of the quantity fulfilling it. Importantly, our theorem overcomes the prototypical assumption of ideal thermal reservoirs. We also study the possibility of split entropy production in arbitrary quantum processes into adiabatic and non-adiabatic contributions, each of them fulfilling an independent fluctuation theorem. Contrary to the classical case, quantum effects may break the split, and we discuss the necessary conditions to enforce it. Our findings are illustrated in three relevant examples for quantum thermodynamics.

Finally, we focus on the role quantum effects in the performance of quantum thermal machines. We analyze the case of an optimized quantum Otto cycle powered by a squeezed thermal reservoir. Our previous results allow us to characterize the many striking nonequilibrium features that arise, including work extraction from a single reservoir or multi-task regimes combining both refrigeration of a cold reservoir and work extraction at the same time. On the other hand, we also explore the role of the Hilbert space dimension in the performance of autonomous quantum thermal machines. Our results point that adding extra levels constitutes a thermodynamical resource. For the case of autonomous fridges, we further obtain a statement on the third law of thermodynamics in terms of their number of levels: reaching zero temperature requires an infinite Hilbert space dimension.

The research results presented in this thesis are complemented with a broad introduction to the field of open quantum systems and quantum thermodynamics. There, we review the state of the art on these topics and the reader will find the main methods and tools used along the thesis.