Validity of Generalized Second Law of Thermodynamics in Rastall Cosmology: Generalized Chaplygin Gas with Tsallis Entropy.

In this study, we analyze the cosmological dynamics and thermodynamic features of the universe using Rastall gravity and the generalized Chaplygin gas (GCG) model, as well as Tsallis entropy. The goal of this analysis is to better comprehend the role of modified gravity and non-extensive thermodynamics in explaining the observed accelerated expansion of the universe. The behavior of the effective equation-of-state parameter is investigated in depth, and the results show that the model can describe both quintessence-like and phantom regimes at various periods of cosmic evolution. To investigate the universe's expansion history, two types of scale factors, power-law and hybrid, are explored. Among them, the hybrid scale factor provides a more realistic picture of the universe by accurately replicating the shift from an early decelerated phase to the current accelerated phase of expansion. Tsallis entropy is used to investigate the validity of the generalised second law of thermodynamics. The research shows that the generalized second rule holds true throughout the evolutionary history of the universe, showing that the proposed model is thermodynamically consistent. Furthermore, observational restrictions are applied using the most recent Hubble parameter H(z) data. Confidence contour analysis is used to define the model parameters' allowable ranges and evaluate their compliance with observations. The acquired results indicate that the suggested Rastall gravity model, when combined with generalized Chaplygin gas and Tsallis entropy, provides a realistic and observationally compatible framework for characterizing the large-scale evolution and accelerated expansion of the universe.