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Modular Time Evolution and the QNEC
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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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Cited by 1 Pith paper
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Black hole thermodynamics at null infinity. Part 1: Dual Generalized Second Law
At future null infinity, the generalized second law for a Schwarzschild black hole becomes the monotonic decrease of a free energy, or grand potential, constructed from the Bondi mass and angular-mode chemical potentials.
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