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.
Relative Entropy and Holography
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful equation $\Delta S=\Delta H$ for the first order variation of the entanglement entropy $\Delta S$ and the expectation value of the \modu Hamiltonian $\Delta H$. We evaluate relative entropy between the vacuum and other states for spherical regions in the AdS/CFT framework. We check that the relevant equations and inequalities hold for a large class of states, giving a strong support to the holographic entropy formula. We elaborate on potential uses of the equation $\Delta S=\Delta H$ for vacuum state tomography and obtain modified versions of the Bekenstein bound.
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The metric is reinterpreted as relational information carried by local correlations with a quantum reference frame, yielding the nonlinear Einstein equation via a conditional entropy constraint with scalar curvature equal to the cosmological constant.
Convexity of non-commutative L^p norms yields bounds on relative entropy for arbitrary excitations of faithful states in general von Neumann algebras, with uniform boundedness proven for single-particle states of the chiral current.
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
Holographic calculation of longitudinal and transverse diffusion coefficients for Brownian motion in a boosted AdS black brane, with verification of the fluctuation-dissipation theorem and expression of the coefficients via butterfly velocity.
Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.
citing papers explorer
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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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Recovering Einstein's equation from local correlations with quantum reference frames
The metric is reinterpreted as relational information carried by local correlations with a quantum reference frame, yielding the nonlinear Einstein equation via a conditional entropy constraint with scalar curvature equal to the cosmological constant.
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Bounding relative entropy for non-unitary excitations in quantum field theory
Convexity of non-commutative L^p norms yields bounds on relative entropy for arbitrary excitations of faithful states in general von Neumann algebras, with uniform boundedness proven for single-particle states of the chiral current.
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Multi-entropy in heavy local quenches
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
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Holographic Brownian dynamics of a heavy particle in a boosted thermal plasma background
Holographic calculation of longitudinal and transverse diffusion coefficients for Brownian motion in a boosted AdS black brane, with verification of the fluctuation-dissipation theorem and expression of the coefficients via butterfly velocity.
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Black hole chemistry: thermodynamics with Lambda
Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.