Testing the Generalized Second Law in $(2+1)$-Dimensional Cosmology: Holographic Entropy Bounds and Observational Constraints

TL;DR

This paper tests the Generalized Second Law of thermodynamics in a (2+1)-dimensional holographic universe, analyzing entropy bounds and using observational data to constrain the model, finding the Hubble Entropy bound more consistent with the GSL.

Contribution

It provides a theoretical comparison of two entropy bounds in (2+1)-dimensional cosmology and uses observational data to evaluate their validity and robustness.

Findings

Fischler--Susskind bound incompatible with GSL in contracting universes

Hubble Entropy bound consistent with GSL in expanding universes

Quantum corrections can reconcile the HE bound in some contracting scenarios

Abstract

We investigate the validity of the Generalized Second Law (GSL) of thermodynamics in a $(2+1)$-dimensional holographic cosmological model with a negative cosmological constant. Adopting a horizon thermodynamics framework, we examine two prominent entropy bounds, the Fischler--Susskind (FS) bound and the Hubble Entropy (HE) bound, in both expanding and contracting universes, including the effects of quantum entropy corrections. Our theoretical analysis shows that the FS bound is intrinsically incompatible with the GSL in contracting $(2+1)$-dimensional universes, regardless of spatial curvature or exotic matter content, and that this incompatibility persists even when quantum corrections are considered. In contrast, the HE bound is consistent with the GSL in expanding universes under classical conditions and can also be reconciled in certain contracting scenarios when quantum effects are included. To complement the theoretical study, we perform a Markov Chain Monte Carlo (MCMC) analysis using recent Baryon Acoustic Oscillations (BAO), Cosmic Chronometer (CC), and Hubble parameter datasets to constrain the model parameters. The best-fit results reveal good cross-dataset consistency, with the cosmological constant parameter $\psi$ remaining stable across all probes. These findings identify the HE bound as a more robust candidate for holographic constraints in lower-dimensional cosmology, while demonstrating the limitations of the FS bound. Our results not only clarify the status of the GSL in $(2+1)$-dimensional settings but also provide a framework for testing entropy bounds with future high-precision cosmological data.