Many-body effects in finite-time quantum thermodynamic processes

As in the classical world, thermodynamics will impose limits in the fabrication and operation of devices for quantum technologies [1]. The descriptions and the laws as formulated within the conventional thermodynamics are no longer valid at the scales where these technologies are being developed [2]. 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 [3]. Recently we presented methods to calculate quantum thermodynamic properties of interacting systems subject to driving fields [4], where there were applied to the calculation of the average quantum 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 [5], 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 a finite-time – not quenched – processes. Following these initial results, in this project 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.
[1] See e.g., John Goold, Marcus Huber, Arnau Riera, Lídia del Rio, and Paul Skrzypczyk. The role of quantum information in thermodynamics-a topical review. J. Phys. A: Math. Theor., 49(14):143001, 2016; Sai Vinjanampathy and Janet Anders. Quantum thermodynamics. Contemp. Phys., 57(4):545, 2016.
[2] D Castelvecchi. Battle between quantum and thermodynamic laws heats up. Nature, 543(7647):597, 2017
[3] See e.g. Ming Zhong and Peiqing Tong. Work done and irreversible entropy production in a suddenly quenched quantum spin chain with asymmetrical excitation spectra. Phys. Rev. E, 91(3):032137, 2015; Jens Eisert, et al.. Quantum many-body systems out of equilibrium. Nat. Phys., 11(2):124, 2015; Alison Leonard and Sebastian Deffner. Quantum work distribution for a driven diatomic molecule. Chem. Phys., 446:18–23, 2015; E Solano-Carrillo and AJ Millis. Theory of entropy production in quantum many-body systems. Phys. Rev. B, 93(22):224305, 2016.
[4] M. Herrera, R. M. Serra, and I. D’Amico. DFT-inspired Methods for Quantum Thermodynamics. Scientific Reports 7, Article number 4655 (2017); Herrera, M., Zawadzki, K. & D’Amico I.. Melting a Hubbard dimer: benchmarks of ALDA for quantum thermodynamics. Eur. Phys. J. B (2018) 91: 248.; A H Skelt, K Zawadzki and I D’Amico. Many-body effects on the thermodynamics of closed quantum systems. J. Phys. A: Math. Theor. 52 485304 (2019).
[5] Krissia Zawadzki, Roberto M. Serra, Irene D’Amico. Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time. Phys. Rev. Research 2, 033167 (2020); arXiv:1908.06488