Notes on Spacetime Thermodynamics and the Observer-dependence of Entropy

TL;DR

This paper examines how different observers, due to the Unruh effect, assign varying entropies to objects crossing horizons, revealing that accelerated observers' entropy estimates are bounded even as internal states grow large.

Contribution

It demonstrates the observer-dependent nature of entropy in spacetime thermodynamics, especially highlighting the bounded entropy for accelerated observers in the large internal states limit.

Findings

Accelerated observers assign bounded entropy as internal states increase.

Inertial observers' entropy estimates differ significantly from accelerated observers.

Implications for the generalized second law and entropy bounds are discussed.

Abstract

Due to the Unruh effect, accelerated and inertial observers differ in their description of a given quantum state. The implications of this effect are explored for the entropy assigned by such observers to localized objects that may cross the associated Rindler horizon. It is shown that the assigned entropies differ radically in the limit where the number of internal states $n$ becomes large. In particular, the entropy assigned by the accelerated observer is a bounded function of $n$. General arguments are given along with explicit calculations for free fields. The implications for discussions of the generalized second law and proposed entropy bounds are also discussed.