Fluctuations of subsystem entropies at late times

Journal Article · 13 February 2022 · Physical Review A

DOI: https://doi.org/10.1103/physreva.105.022416 · OSTI ID:1979608

Cotler, Jordan  ^[1]; Hunter-Jones, Nicholas ^[2]; Ranard, Daniel ^[3]

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1. Harvard Univ., Cambridge, MA (United States); OSTI
2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
3. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics

We study the fluctuations of subsystem entropies in closed quantum many-body systems after thermalization. Using a combination of analytics and numerics for both random quantum circuits and Hamiltonian dynamics, we find that the statistics of such entropy fluctuations is drastically different than in the classical setting. For instance, shortly after a system thermalizes, the probability of entropy fluctuations for a subregion is suppressed in the dimension of the Hilbert space of the complementary subregion. This suppression becomes increasingly stringent as a function of time, ultimately depending on the exponential of the Hilbert space dimension, until extremely late times when the amount of suppression saturates. We also use our results to estimate the total number of rare fluctuations at large timescales. We find that the “Boltzmann brain” paradox is largely ameliorated in quantum many-body systems, in contrast with the classical setting.

• Research Organization: Harvard Univ., Cambridge, MA (United States); Univ. of California, Oakland, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0007870; SC0019380
• OSTI ID: 1979608
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 105; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English