Modular Time Evolution and the QNEC

Abstract

We establish an inequality restricting the evolution of states in quantum field theory with respect to the modular flow of a wedge, $\hat{I}{”}^{is}$, 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'' $\le 2\ddot{I}€$ 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.

18 pages, no figures