Many-body effects in finite-time quantum thermodynamic processes

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As in the classical world, thermodynamics will impose limits in the fabrication and operation of devices for quantum technologies. The descriptions and the laws as formulated within the conventional thermodynamics are no longer valid at the scales where these technologies are being developed. At this level energy fluctuations become important, and quantities such as work, heat, and entropy production are treated as stochastic variables. The study of the thermodynamics of quantum many-body systems remains a challenging task, as even theoretical studies may require an enormous computational power. The investigation of the thermodynamics of the emergent collective phenomena in quantum many-body systems is, without a doubt, a fascinating subject. Some discussions about quantum thermodynamic properties in many-body out-of-equilibrium systems have been reported. Recently we presented methods to calculate quantum thermodynamic properties of interacting systems subject to driving fields, where there were applied to the calculation of the averagequantum work and entropy in a Hubbard model driven by a time-dependent external potential. We also started analysing signatures of the metal- Mott-insulator transition, a many-body-driven quantum-phase transitions, in finite-time quantum thermodynamic processes, and demonstrate how increasing correlations dramatically affect the statistics of energy fluctuations and consequently the quantum work distribution of finite Hubbard chains. In particular we noted distinct effects due to the considered processes being afinite-time - not quenched - processes. Following these initial results, in thisproject we wish to capture a more general understanding of the signatures of quantum phase transitions on quantum thermodynamic properties. To this aim we will consider results from different quantum phase transitions during processes driven by various time-dependent potentials. A particular aim is to identify how finite-time processes modify the character of such signatures.