# A Lower Bound on the Energy Density in Classical and Quantum Field Theories

## TL;DR

This paper introduces a new method to derive energy bounds in classical and quantum field theories, revealing a universal local energy condition in classical theories and a quantum energy condition linked to information theory.

## Contribution

It presents a novel approach to establish energy conditions in stable field theories, including a quantum energy bound dependent on information-theoretic measures.

## Key findings

- Existence of a local energy condition in 1D classical theories
- Derivation of the dominant energy condition in relativistic theories
- Quantum energy condition as a lower bound involving information measures

## Abstract

A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant energy condition. In a quantum field theory, there instead exists a quantum energy condition, i.e. a lower bound on the energy density that depends on information-theoretic quantities. Some extensions to higher dimensions are briefly discussed.