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Time evolution of entanglement for holographic steady state formation. (English) Zbl 1383.81207

Summary: Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time \(t=0\). A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T28 Thermal quantum field theory
80A10 Classical and relativistic thermodynamics
81P40 Quantum coherence, entanglement, quantum correlations
83C80 Analogues of general relativity in lower dimensions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

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