Modular Time Evolution and the QNEC

Stefan Hollands

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arXiv · 2503.21385

Modular Time Evolution and the QNEC

Stefan Hollands

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Abstract

We establish an inequality restricting the evolution of states in quantum field theory with respect to the modular flow of a wedge, $\Delta^{is}$, for large $|s|$. Our bound is related to the quantum null energy condition, QNEC. In one interpretation, it can be seen as providing a ``chaos-bound'' $\le 2\pi$ on the Lyapunov exponent with respect to Rindler time, $s$. Mathematically, our inequality is a statement about half-sided modular inclusions of von Neumann algebras.

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Stefan Hollands. 2025-03-27. Modular Time Evolution and the QNEC. https://arxiv.org/abs/2503.21385

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