arXiv subjects

V. R. Shajiee

Publications and source records attributed to V. R. Shajiee.

3 recordsLinked to original sources

arXiv2026

Gravitational Entropy And The Second Law of Thermodynamics for Causal Observers

It is well established that black holes possess entropy and behave as thermodynamic systems. Associating entropy with gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in gravitating systems. There have been many ideas and attempts to prove the second law within gravitating systems starting from first principles. Within the covariant phase space formalism, we define gravitational entropy as the charge associated with the local boosts, detaching the gravitational entropy from horizons or trapped surfaces as well as from the diffeomorphisms as symmetry generators. Using this definition for the Einstein gravity case, we compute variations of the entropy along the path of any causal free-fall observer and establish that the entropy variations are always non-negative if the matter content satisfies the strong energy condition integrated along any segment of the observer's trajectory.

hep-th↗

arXiv2026

Who Writes the Gravitational Second Law of Thermodynamics?

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.

hep-th↗

arXiv2026

Dynamical Entropy Is a Noether Charge

Black hole thermodynamics for generic dynamical, non-equilibrium regimes remains a fundamental challenge. We establish dynamical entropy as the Noether charge associated with a generic evolving null surface subject to Dirichlet boundary conditions. We specify the symmetry generator associated with the dynamical entropy, which is a null vector on the null surface, upon requiring physically motivated geometric conditions that yield a notion of ``dynamical zeroth law.'' We prove that this Noether charge density satisfies the second law of thermodynamics strictly at each instant in time, bypassing the teleological final conditions traditionally required by event horizons. Thus, we extend and generalize the notion of dynamical entropy introduced in \cite{Hollands:2024vbe}, in some different ways: We do not impose background stationarity; our dynamical entropy and the associated second law are local in time and work for generic dynamical gravitational systems.

hep-th↗