Entropy in Loop Quantum Cosmology

The Generalized First Law (GFL) and the Generalized Second Law (GSL) of thermodynamics are studied for cosmological scenarios with spatial curvature through an apparent horizon. We focus on effective and alternative cosmic systems motivated by quantum cosmological models, where the entropy is considered a function of the apparent area, transforming the effective cosmological model into the standard form in cosmology. The general conditions for the validity of the GSL are analyzed for entropy as a general function of area and logarithmic corrections to the usual Black Hole entropy. The Weak Energy Condition (WEC) and the Strong Energy Condition (SEC) are implemented for the matter entropy part. In particular, we study the GFL and the regions where the GSL is valid for effective Loop Quantum Cosmology (LQC) models with spatial curvature $k=0,\pm 1$, taking every possible value of the logarithmic contributing factor for the entropy analysis. In addition, in order to solve some violations of the GSL, we explore the possibility of admitting negative absolute temperatures (NAT) in our system, where the validity conditions for an extended generalized second law (EGSL) are studied, and the time arrow from the second law is discussed for the LQC models.