The generalized second law of thermodynamics in viscous Ricci dark energy model

In this paper, we study the validity of the generalized second law of thermodynamics by applying Bekestein–Hawking (BH) entropy and Barrow entropy for the horizon entropy, respectively in the viscous holographic Ricci dark energy (HRDE) model. The background is a spatially flat Friedmann–Robertson–Walker universe filled with pressureless dark matter and viscous HRDE. The bulk viscous coefficient is assumed to be ζ=ζ0+ζ1H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta =\zeta _0+\zeta _1 H$$\end{document}. In first step, we find the analytical solution of the field equations of viscous HRDE model. We use the observational data from SNe, OHD and BAO/CMB in order to extract the constraints on viscous HRDE model. In second step, we calculate the entropy time-variation for each fluid component and for the apparent horizon itself. In BH entropy case, the sum of the entropy of the fluids (viscous HRDE and dark matter) enclosed by the apparent horizon plus the entropy of the horizon itself is non-decreasing function of time which shows that the generalized second law of thermodynamics is valid. It also satisfies the convexity condition which shows that the model approaches a stable equilibrium thermal state. However, in the case of Barrow entropy, the generalized second law of thermodynamics may be violated as it depends on the universe evolution. Finally, we examine the generalized second law of thermodynamics of viscous HRDE model by taking into account the Casimir effect and find that it is valid throughout the evolution of the universe.