the cosmological space causally connected as a whole.\
It is now worthwhile to stress a remarkable feature of the obtained solution which makes it essentially different from the same limit treated in [@BK_Bianchi]. Indeed, there, the isotropic solution was considered for $t\rightarrow 0_-$ simply because it corresponds to a singular point in the dynamical system approach of equations (\[H\]), (\[H\_punto\]), (\[rho\_punto\]) and (\[integrale2\]). Here we deal with increasing $t$ values and our dynamics describes an expanding universe from the initial singularity. This choice characterizing the evolution regime is physically allowed when one considers the behavior of the entropy per comoving volume. The latter has the form $$\sigma \sim \rho^{\frac{1}{\gamma}}R^{3}\sim t^{2 \left(\frac{1}{\gamma_{eff}}-\frac{1}{\gamma}\right)}.$$ Since from equation (\[gamma1\]) we see that $$\label{gamma2}
  \gamma=\gamma_{eff} \left[\frac{1}{1-4\beta_{2}(2\beta_{2}+1)^{\beta_{2}}\frac{\zeta_{1}R_{0}^{3}}{(3\chi)^{\beta_{2}}\mu_{0}}}\right]>\gamma_{eff},$$ it is straightforward to infer that the entropy per comoving volume increases due to dissipation processes when the universe expands. This brings us to conclude that we are dealing with a cosmological paradigm in which the universe emerges from the singularity causally connected as a whole and with a significant entropy creation (this effect is enhanced by increasing $\beta_{2}$ values). This suggests how extreme non-equilibrium thermodynamics near the singularity could play a relevant role in solving some unpleasant paradoxes 