Who Writes the Gravitational Second Law of Thermodynamics?
Abstract
We define gravitational entropy as the manifestly integrable surface charge associated with local transverse Lorentz boosts, entirely bypassing the conventional reliance on spacetime diffeomorphisms. Any notion of entropy must satisfy the second law. To answer the question posed in the title, an analogy with Newtonian classical mechanics is instructive: Newton's second law of motion is written by inertial observers who are defined by the first law of mechanics. We show that the second law of gravitational thermodynamics is written by free-fall observers with path parameterization in which the non-affinity of the geodesics is equal to the expansion of their velocity vector field. We then provide a proof of the local second law by studying variations in entropy as viewed by this class of covariantly-defined causal free-fall observers. We show that the entropy variation is strictly non-decreasing, provided the matter sector satisfies the integrated strong energy condition along the observer path.
Related
- Second Law of Thermodynamics in Closed Quantum Many-Body Systems
- Generic thermodynamics of condensates with extremely small superfluid density ---Application to UTe2 and hidden second phase transition---
- Ghost-free higher-gradient Newtonian gravity from the Second Law of Thermodynamics
- Deriving the second law of thermodynamics and exploring its boundaries
- Particle Dynamics and Thermodynamics of a Charged-Like Hairy Black Hole in Extended Gravitational Decoupling
BibTeX
@misc{shajiee2026writes,
title = {{Who Writes the Gravitational Second Law of Thermodynamics?}},
author = {V. R. Shajiee and M. M. Sheikh-Jabbari and V. Taghiloo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.16997},
eprint = {2608.16997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.16997},
}
RIS
TY - UNPB
TI - Who Writes the Gravitational Second Law of Thermodynamics?
AU - V. R. Shajiee
AU - M. M. Sheikh-Jabbari
AU - V. Taghiloo
PY - 2026
DA - 2026/10/31
PB - arXiv
DO - 10.48550/arxiv.2608.16997
UR - https://arxiv.org/abs/2608.16997
AB - We define gravitational entropy as the manifestly integrable surface charge associated with local transverse Lorentz boosts, entirely bypassing the conventional reliance on spacetime diffeomorphisms. Any notion of entropy must satisfy the second law. To answer the question posed in the title, an analogy with Newtonian classical mechanics is instructive: Newton's second law of motion is written by inertial observers who are defined by the first law of mechanics. We show that the second law of gravitational thermodynamics is written by free-fall observers with path parameterization in which the non-affinity of the geodesics is equal to the expansion of their velocity vector field. We then provide a proof of the local second law by studying variations in entropy as viewed by this class of covariantly-defined causal free-fall observers. We show that the entropy variation is strictly non-decreasing, provided the matter sector satisfies the integrated strong energy condition along the observer path.
ER -