Defining Entropy Bounds

TL;DR

This paper explores new definitions for entropy bounds in quantum field theories, addressing previous counterexamples and discussing challenges in extending these concepts to gravitational theories.

Contribution

It proposes novel, more precise definitions for system size, energy, and entropy in nongravitational quantum field theories, improving the understanding of entropy bounds.

Findings

New definitions for R, E, and S in quantum field theories.

Identification of difficulties in extending entropy bounds to gravitational theories.

Analysis of counterexamples to Bekenstein's entropy bound.

Abstract

Bekenstein's conjectured entropy bound for a system of linear size R and energy E, S < 2 pi E R, has counterexamples for many of the ways in which the "system," R, E, and S may be defined. Here new ways are proposed to define these quantities for arbitrary nongravitational quantum field theories in flat spacetime, such as defining R as the smallest radius outside of which only vacuum expectation values occur. Difficulties of extending these definitions to gravitational quantum theories are noted.