| Summary: | Thermal machines have played a historic role in enhancing our understanding of thermodynamics. Quantum thermal machines, which o↵er unique properties with no classical counterpart, such as coherence, entanglement and quantum collective effects, promise to replicate this success and provide insight into how the laws of thermodynamics extend to atomistic length and energy scales. Recently, success has been found in considering slowly driven microscopic engines, whose useful thermodynamic quantities such as power and efficiency, can be understood and related to each other in the form of trade-o↵ relations, in the so-called adiabatic response regime. Additional thermodynamic figures of merit such as constancy, which characterises the reliability of microscopic thermal machines against thermal and quantum fluctuations, play an important role at this energy scale and can also be included in this adiabatic response limit.
In this thesis we aim to capitalise on the adiabatic response framework and derive results which quantify the performance of quantum thermal machines that are driven by slow external control. We employ the framework of thermodynamic geometry, which relates thermodynamic measures to geometric quantities, in the space of the control parameters that are modulated to realise an engine cycle. Here, we derive a universal trade-off relation which decays quadratically in power as the fundamental upper bound on performance is approached. Additionally, we extend the geometric picture to consider many-body quantum gases, which can act as the working fluid of small scale engines. In this way, previously derived trade-o↵ relations can be used to compare the collective e↵ects of particular many-body systems. Since realistic thermal machines with practical ways to measure the fluctuations in the input and output are required, we derive a thermodynamically consistent framework which allows us to describe quantum-classical engines, whose output can be traced by the motion of the classical degree of freedom. These devices consist of a quantum system, which is mechanically coupled to a classical system that evolves slowly relative to the characteristic timescale of the quantum working system. These results all rely on the adiabatic response picture, which has proven successful in characterising the operation of slowly driven quantum thermal machines.
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