Two approaches to Quantum Thermodynamics: Small Thermal Machines and Fluctuation Theorems

When considering small systems, quantum fluctuations, in addition to thermal ones, come into play. Furthermore there is a wide range of phenomena without classical counterpart that cannot be neglected, such as coherence, squeezing or entanglement, in both single and many-body systems. One of the purposes of Quantum Thermodynamics is extending both equilibrium an non-equilibrium thermodynamic notions beyond the classical regime. In this seminar I will focus in two promising routes to the understanding of thermodynamics in quantum systems: small thermal machines and non-equilibrium fluctuation relations. The first one explores questions about the minimum size of heat engines, the possible limitations arising on their performance and the nature of work in self-contained quantum settings. The second one establishes exact statements about the fluctuations of thermodynamical quantities in systems arbitrarily far from equilibrium.