Landauer entropy of spacetime

TL;DR

This paper introduces a geometric definition of spacetime entropy based on Landauer's principle, linking it to Bekenstein-Hawking entropy and establishing a second law under specific conditions.

Contribution

It provides a novel geometric framework for defining spacetime entropy and relates it to established black hole entropy concepts.

Findings

Defined a surface integral-based entropy for static, spherically symmetric spacetimes.

Established a second law for the Landauer entropy under mild assumptions.

Connected the Landauer entropy to Bekenstein-Hawking entropy.

Abstract

Based on Landauer's principle, we provide a geometrical definition for the entropy of a given static, spherically symmetric spacetime. Considering a congruence of geodesics across a surface, one defines the entropy of a congruence as the surface integral of the entropy of the constituent geodesics. Under certain mild assumptions, we establish a second law for the entropy function thus defined (Landauer entropy), and relate it to Bekenstein-Hawking entropy.