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Note on entropy dynamics in the Brownian SYK model

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arxiv 2011.08158 v2 pith:TKXFKPHR submitted 2020-11-16 cond-mat.stat-mech cond-mat.str-elhep-thquant-ph

Shao-Kai Jian , Brian Swingle This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.str-elhep-thquant-ph
keywords entropydynamicsbrownianenyianalysiscurveequationintegral
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We study the time evolution of R\'enyi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The R\'enyi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of R\'enyi entropy, respectively.

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  1. Replica Wormholes, Modular Entropy, and Capacity of Entanglement in JT Gravity

    hep-th 2025-01 conditional novelty 4.0 of 10

    In JT gravity toy models, late-time modular entropy and capacity of entanglement scale inversely with n times the inverse temperature, supporting a thermal reading of the replica parameter.

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