From Quantum Relative Entropy to the Semiclassical Einstein Equations

[Submitted connected 28 Oct 2025 (v1), past revised 3 Mar 2026 (this version, v3)]

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Abstract:We supply arguments indicating that the semiclassical Einstein equations travel from quantum comparative entropy and its proportionality to an area variation. Using modular theory, we found that the comparative entropy betwixt the vacuum authorities and coherent excitations of a scalar quantum section connected a bifurcate Killing sky is fixed by the power flux crossed the horizon. Under the presumption of the Bekenstein-Hawking entropy-area formula, this power flux is proportional to a variety successful the aboveground area of the sky transverse section. The semiclassical Einstein equations travel automatically from this identification. Our attack provides a quantum section theoretic generalization of Jacobson's thermodynamic derivation of the Einstein equations, replacing classical thermodynamic entropy pinch the well-defined quantum comparative (Araki-Uhlmann) entropy. This suggests that quantum accusation plays a cardinal domiciled successful what is often seen arsenic a zeroth bid approximation of a mentation of quantum gravity, namely quantum section mentation successful curved spacetimes.