Generalised second law beyond the semiclassical regime

TL;DR

This paper proves the generalized second law (GSL) holds in perturbative gravity beyond the semiclassical limit without UV cutoff, using algebraic techniques and introducing dynamical cuts as quantum reference frames.

Contribution

It extends the proof of the GSL to all orders in perturbative gravity without UV restrictions by employing null translation invariance and dynamical cuts.

Findings

GSL holds in perturbative gravity beyond semiclassical limit

Introduction of dynamical cuts as quantum reference frames

Reduction to standard GSL under semiclassical and energy conditions

Abstract

We prove that the generalised second law (GSL), with an appropriate modification, holds in perturbative gravity to all orders beyond the semiclassical limit and without a UV cutoff imposed on the fields. Our proof uses algebraic techniques and builds on the recent work of Faulkner and Speranza, which combined Wall's proof of the GSL with the identification of generalised entropy as the von Neumann entropy of a boost-invariant crossed product algebra. The key additional step in our approach is to further impose invariance under null translations. Doing so requires one to describe horizon exterior regions in a relational manner, so we introduce `dynamical cuts': quantum reference frames which give the location of a cut of the horizon. We use idealised dynamical cuts, but expect that our methods can be generalised to more realistic models. The modified GSL that we prove says that the difference in generalised entropies of the regions outside two dynamical cuts is bounded below by the free energy of the degrees of freedom giving the location of the later cut. If one takes a semiclassical limit, imposes a UV cutoff, and requires the cuts to obey certain energy conditions, then our result reduces to the standard GSL.