Abstract
We study the dynamics of a quantum system in thermal equilibrium that is suddenly coupled to a bath at a different temperature, a situation inspired by a particular black hole evaporation protocol. We prove a universal positivity bound on the integrated rate of change of the system energy which holds perturbatively in the system-bath coupling. Applied to holographic systems, this bound implies a particular instance of the averaged null energy condition. We also study in detail the particular case of two coupled SYK models in the limit of many fermions using the Schwinger-Keldysh non-equilibrium formalism. We solve the resulting Kadanoff-Baym equations both numerically and analytically in various limits. In particular, by going to low temperature, this setup enables a detailed study of the evaporation of black holes in JT gravity.
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Acknowledgments
We would like to thank Juan Maldacena for many comments and discussions. It’s a pleasure to thank Alexander Abanov, Ksenia Bulycheva, Yiming Chen, Alexander Gorsky, Alex Kamenev, Dmitri Kharzeev, Ho Tat Lam, Fedor Popov, Jacobus Verbaarschot, Douglas Stanford, Zhenbin Yang for helpful comments on this topic. A.A. is supported by funds from the Ministry of Presidential Affairs, UAE. BGS is supported by the Simons Foundation via the It From Qubit collaboration.
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Almheiri, A., Milekhin, A. & Swingle, B. Universal constraints on energy flow and SYK thermalization. J. High Energ. Phys. 2024, 34 (2024). https://doi.org/10.1007/JHEP08(2024)034
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DOI: https://doi.org/10.1007/JHEP08(2024)034