Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
Entropic interpretation of Ein- stein equation in dS/CFT,
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Scalar hair breaks the time-independence of imaginary HTEE, introduces nontrivial Δt dependence, causes analytic continuation to fail, and makes timelike subregion complexity real-valued with interior-only UV-finite contributions in BTZ.
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Real-time pseudo entropy and modular-Hamiltonian correlations
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
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Holographic timelike entanglement and subregion complexity with scalar hair
Scalar hair breaks the time-independence of imaginary HTEE, introduces nontrivial Δt dependence, causes analytic continuation to fail, and makes timelike subregion complexity real-valued with interior-only UV-finite contributions in BTZ.