A. Shahriar, M. Abbasiyan-Motlaq, M. Mohsenzadeh, E. Yusofi

This paper introduces a cosmological model that incorporates the simultaneous merger process for evolving dark energy and evolving dark matter and analyzes its Hubble parameter behavior. To validate this model, we assess the applicability of the generalized second law of thermodynamics and the maximum entropy condition within this framework. We derive a generalized form of the Hubble parameter for this model, demonstrating that it converges to the standard Hubble parameter in the non-merger case (\(\xi = 0\)). The merging model's equation of state parameters resembles those of evolving dark matter and dark energy, with \(w_c(z) \simeq w_{\rm dm} \simeq 0\) and \(w_v(z) \simeq w_{\rm de} \simeq -1\) at $z\rightarrow 0$, aligning with recent observations. We attribute the roles of dynamical dark matter and dark energy to super-voids and super-clusters, the largest merging objects in the web-like universe. We compare our model by analyzing the Hubble parameter and the entropy along with its first and second derivatives for the $w$CDM and standard $\Lambda$CDM models. Our plots indicate that the models incorporating only cluster mergers exhibit greater discrepancies with both observational Hubble parameters and the standard model at $z > 1$. A key finding is that in models featuring only cluster mergers, Hubble and entropy rates consistently decrease. Furthermore, we demonstrate that the $\Lambda$CDM model with both additive and non-additive entropy violates the convexity condition, whereas the merger voids model aligns with maximizing entropy and at the same time may help avert a \textit{Big Rip} scenario for our universe.