Relative entropy and the Bekenstein bound

TL;DR

This paper connects quantum field theory and statistical mechanics to the Bekenstein bound using relative entropy, proposing a formulation that holds automatically in flat space and clarifies its physical implications.

Contribution

It introduces a new interpretation of the Bekenstein bound via relative entropy between vacuum and other states, avoiding the species problem and clarifying its semiclassical relevance.

Findings

Relative entropy positivity encodes the Bekenstein bound in flat space.

The formulation naturally arises from the generalized second law with quantum effects.

The bound does not impose new constraints at the semiclassical level.

Abstract

Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum and another state, both reduced to a local region. We propose that, with the adequate interpretation, the positivity of the relative entropy in this case constitutes a well defined statement of the bound in flat space. We show that this version arises naturally from the original derivation of the bound from the generalized second law when quantum effects are taken into account. In this formulation the bound holds automatically, and in particular it does not suffer from the proliferation of the species problem. The results suggest that while the bound is relevant at the classical level, it does not introduce new physical constraints semiclassically.