Abstract
The dynamics when a hot many-body quantum system is brought into instantaneous contact with a cold many-body quantum system can be understood as a combination of early time quantum correlation (von Neumann entropy) gain and late time energy relaxation. We show that at the shortest timescales there is an energy increase in each system linked to the entropy gain, even though equilibrium thermodynamics does not apply. This energy increase is of quantum origin and results from the collective binding energy between the two systems. Counter-intuitively, this implies that also the hotter of the two systems generically experiences an initial energy increase when brought into contact with the other colder system. In the limit where the energy relaxation overwhelms the (quantum) correlation build-up, classical energy dynamics emerges where the energy in the hot system decreases immediately upon contact with a cooler system. We use both strongly correlated SYK systems and weakly correlated mixed field Ising chains to exhibit these characteristics, and comment on its implications for both black hole evaporation and quantum thermodynamics.
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Acknowledgments
We thank Jan Zaanen for discussions in the early stage of this project and we thank Sebastian Deffner and Akram Touil for discussions. This research was supported in part by the Netherlands Organization for Scientific Research/Ministry of Science and Education (NWO/OCW), by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme. The numerical calculations were performed on the ALICE High Performance Computing facility of the Leiden University and Leiden University Medical Center.
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Ohanesjan, V., Cheipesh, Y., Gnezdilov, N.V. et al. Energy dynamics, information and heat flow in quenched cooling and the crossover from quantum to classical thermodynamics. J. High Energ. Phys. 2023, 237 (2023). https://doi.org/10.1007/JHEP05(2023)237
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DOI: https://doi.org/10.1007/JHEP05(2023)237