Modular energy inequalities from relative entropy

TL;DR

This paper derives new quantum energy inequalities using the monotonicity of relative entropy, linking energy density and entropy constraints in quantum field theories, especially conformal field theories.

Contribution

It introduces novel constraints on modular energy based on relative entropy, improving bounds on energy density and negative energy in quantum field theories.

Findings

New bounds for energy density in conformal field theories

Constraints linking entropy and negative energy

Enhanced quantum energy inequalities

Abstract

We obtain new constraints for the modular energy of general states by using the monotonicity property of relative entropy. In some cases, modular energy can be related to the energy density of states and these constraints lead to interesting relations between energy and entropy. In particular, we derive new quantum energy inequalities that improve some previous bounds for the energy density of states in a conformal field theory. Additionally, the inequalities derived in this manner also lead us to conclude that the entropy of the state further restricts the possible amount of negative energy allowed by the theory.