Quantum Relative Entropy implies the Semiclassical Einstein Equations
- URL: http://arxiv.org/abs/2510.24491v1
- Date: Tue, 28 Oct 2025 15:05:57 GMT
- Title: Quantum Relative Entropy implies the Semiclassical Einstein Equations
- Authors: Philipp Dorau, Albert Much,
- Abstract summary: We prove that the semiclassical Einstein equations emerge directly from quantum information theory.<n>This suggests that quantum information plays a fundamental role in what is seen as a zeroth order approximation of a theory of quantum gravity.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We prove that the semiclassical Einstein equations emerge directly from quantum information theory. Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon. Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section. The semiclassical Einstein equations follow automatically from this identification. Our approach provides a rigorous quantum field theoretic generalization of Jacobson's thermodynamic derivation of Einstein's equations, replacing classical thermodynamic entropy with the well-defined quantum relative (Araki-Uhlmann) entropy. This suggests that quantum information plays a fundamental role in what is seen as a zeroth order approximation of a theory of quantum gravity, namely quantum field theory in curved spacetimes.
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