A note on entropy of matter in presence of gravity: status of extensivity of entropy

TL;DR

This paper investigates how strong gravity influences the entropy of matter, showing that entropy depends on the system's cross-sectional area and discussing the extensivity of entropy in different gravitational regimes.

Contribution

It demonstrates that in strong gravity, entropy is area-dependent and explores the extensivity of entropy in ultra-relativistic gases without gravity, providing new insights into gravitational effects on thermodynamics.

Findings

Entropy depends on cross-sectional area under strong gravity.

Extensivity of entropy is analyzed for ultra-relativistic gases without gravity.

Microscopic degrees of freedom are effectively contributed by the system's area.

Abstract

Entropy of matter in a very strong gravity depends on cross-sectional area of the container of the system -- is being further bolstered by calculating entropy of a monoatomic gas kept under uniform strong gravity at Newtonian scale. This bypasses the earlier analysis where existence of horizon is crucial. Also the extensivity of this entropy has been discussed in the light of the same of a two-space dimensional ultra-relativistic non-interacting gas without gravity. The whole analysis, as far as entropy is concerned, indicates that under strong gravity the microscopic degrees of freedom of the system are effectively contributed by the cross-sectional area of the system.