A few words on Entropy, Thermodynamics, and Horizons

TL;DR

This paper reviews recent advances in black hole thermodynamics, emphasizing the observer-dependent nature of entropy and challenging the necessity of entropy bounds for semi-classical consistency.

Contribution

It introduces the idea that black hole entropy depends on the observer and discusses mechanisms ensuring thermodynamic consistency without entropy bounds.

Findings

Entropy flux varies with the observer crossing the horizon.

Large entropy states are exponentially favored in thermal emissions.

Numerical models support observer-dependent entropy measurements.

Abstract

We review recent progress in understanding certain aspects of the thermodynamics of black holes and other horizons. Our discussion centers on various ``entropy bounds'' which have been proposed in the literature and on the current understanding of how such bounds are {\it not} required for the semi-classical consistency of black hole thermodynamics. Instead, consistency under certain extreme circumstances is provided by two effects. The first is simply the exponential enhancement of the rate at which a macrostate with large entropy is emitted in any thermal process. The second is a new sense in which the entropy of an ``object'' depends on the observer making the measurement, so that observers crossing the horizon measure a different entropy flux across the horizon than do observers remaining outside. In addition to the review, some recent criticisms are addressed. In particular, additional arguments and detailed numerical calculations showing the observer dependence of entropy are presented in a simple model. This observer-dependence may have further interesting implications for the thermodynamics of black holes.