• boundary-driven chains
• limit cycle
• non-equilibrium thermodynamics
• quantum spin chains
• quantum thermodynamics

The purpose of this thesis is to design and analyze a new class of quantum thermal machines. The machines are based on a quantum spin chain interacting with two external thermal baths. A chain undergoes a series of thermodynamic cycles and can exchange heat with the reservoirs and produce usable work. Depending on the various parameters, the machine can work in different operation modes: refrigerator, engine, accelerator, and heater. We show that, under general conditions, all possible initializations of a specific system end up in a unique limit cycle after many iterations. The thesis then focuses on studying the thermodynamic properties of such a limit cycle. We begin with an analytical treatment of small systems with two or three qubits. The analytical treatment shows that there are two behaviors shared by the chains that conserve the total magnetization. The first one is a particular dependence of the operation modes on the temperature of the baths, which is identical for all systems; this property will be proved analytically for all chains preserving the magnetization. The second property is a particular factorization of heat, work, and entropy production into two factors: a universal function of the temperatures and a second function of all the other parameters. This thesis develops a framework to study the low-temperature limit and find closed expressions for heat and work of generic chains in such limit. Next, we design an exact-diagonalization algorithm to study longer chains and obtain numerical evidence that a significant class of systems satisfies the factorization property of the thermodynamic quantities. Such property allows us to reduce the complexity of the problem exponentially, permitting computational calculations for very long chains. Finally, we consider a class of classical thermal machines that is the classical analog of our system to shed light on specific properties that were only observed numerically.