Entropy in Loop Quantum Cosmology

TL;DR

The paper develops a general thermodynamic framework for cosmology in which gravitational entropy is an arbitrary function of the apparent horizon area, $S_g=f(A_A/4)$, and derives generalized first and second laws (GFL and GSL) that hold for any effective cosmological model transformable to standard FRW dynamics. It then incorporates logarithmic corrections to the black-hole entropy, $S_g=rac{A_A}{4}+ ilde{ ext{α}}rac{A_A}{...}+eta$, and analyzes how these corrections modify the GFL/GSL, including the definitions of corrected energy and volume, $D E_g$ and $D V_A$. The focus centers on Loop Quantum Cosmology (LQC), especially the flat model, where the modified Friedmann equations yield a quantum bounce and effective density/pressure; the authors map the GSL validity regions across the correction parameter $ ilde{ ext{α}}$, and show that, near the bounce, the standard GSL can fail while a generalized second law with negative temperature (AGSL) can remain valid. The work highlights that horizon choice and thermodynamic definitions crucially influence the allowed regimes, and demonstrates that negative-temperature AGSL can extend thermodynamic consistency into regimes inaccessible to the standard GSL, with implications for quantum-cosmological thermodynamics.

Abstract

The Generalized First Law (GFL) and the Generalized Second Law (GSL) of thermodynamics are searched for effective and alternative cosmic models using the entropy as a function of the apparent area, transforming the effective cosmological model into the standard form in cosmology. The general conditions of the GSL validity are analyzed for the entropy as a general function and for logarithmic corrections to the usual Black Hole entropy. In particular, we study the GFL and the regions where the GSL is valid for an effective Loop Quantum Cosmology model with spatially flat curvature taking every possible value of the logarithmic correction factor. In addition, we explore the possibility of having negative temperature, where the validity conditions for an alternative generalized second law (AGSL) are studied.