# Outer Entropy and Quasilocal Energy

## TL;DR

This paper introduces a new definition of coarse-grained entropy for normal surfaces in spacetime, linking it to a quasilocal energy concept with favorable physical properties.

## Contribution

It proposes a novel entropy measure based on auxiliary extremal surfaces and develops a formalism assuming vanishing stress tensor, connecting entropy to quasilocal energy.

## Key findings

- Entropy is maximized when the auxiliary geometry has zero stress tensor.
- The coarse-grained entropy is positive and monotonic.
- The entropy can be interpreted as a quasilocal energy measure.

## Abstract

We define the coarse-grained entropy of a `normal' surface $\sigma$, i.e., a surface that is neither trapped nor antitrapped. Following Engelhardt and Wall, the entropy is defined in terms of the area of an auxiliary extremal surface. This area is maximized over all auxiliary geometries that can be constructed in the interior of $\sigma$, while holding fixed the spatial exterior (the outer wedge). We argue that the area is maximized when the stress tensor in the auxiliary geometry vanishes, and we develop a formalism for computing it under this assumption. The coarse-grained entropy can be interpreted as a quasilocal energy of $\sigma$. This energy possesses desirable properties such as positivity and monotonicity, which derive directly from its information-theoretic definition.