The Bousso's D-bound entropy for the various possible black hole solutions on a 4-dimensional brane is checked. It is found that the D-bound entropy here is apparently different from that of obtained for the 4-dimensional black hole solutions. This difference is interpreted as the extra loss of information, associated to the extra dimension, when an extra-dimensional black hole is moved outward the observer's cosmological horizon. Also, it is discussed that N -bound entropy is hold for the possible solutions here. Finally, by adopting the recent Bohr-like approach to black hole quantum physics for the excited black holes, the obtained results are written also in terms of the black hole excited states. *

According to Padmanabhan's proposal, the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space may result in the acceleration of Universe expansion through the relation V / t = N sur − N bulk where N bulk and N sur are referred to the degrees of freedom related to the matter and energy content inside the bulk and surface area, respectively (Padmanabhan, arXiv:1206.4916v1, 2012. In this paper, we study the dynamical effect of the extrinsic geometrical embedding of an arbitrary four-dimensional brane in a higher-dimensional bulk space and investigate the corresponding degrees of freedom. Considering the modification of the Friedmann equations arising from a general braneworld scenario, we obtain a correction term in Padmanabhan's relation, denoting the number of degrees of freedom related to the extrinsic geometry of the brane embedded in higher-dimensional spacetime as V / t = N sur − N bulk − N extr where N extr is for the degree of freedom related to the extrinsic geometry of the brane, while N sur and N bulk are defined as before. Finally, we study the validity of the first and second laws of thermodynamics for this general braneworld scenario in the state of thermal equilibrium and in the presence of confined matter fields to the brane with the induced geometric matter fields.

Based on Padmanabhan's proposal, the accelerated expansion of the universe can be driven by the difference between the surface and bulk degrees of freedom in a region of space, described by the relation dV /dt = N sur − N bulk where N sur and N bulk = −N em + N de are the degrees of freedom assigned to the surface area and the matter-energy content inside the bulk such that the indices "em" and "de" represent energy-momentum and dark energy, respectively. In the present work, the dynamical effect of the Weyssenhoff perfect fluid with intrinsic spin and its corresponding spin degrees of freedom in the framework of Einstein-Cartan (EC) theory are investigated. Based on the modification of Friedmann equations due to the spin-spin interactions, a correction term for Padmanabhan's original relation dV /dt = N sur +N em −N de including the number of degrees of freedom related with these spin interactions is obtained through the modification in N bulk term as N bulk = −N em + N spin + N de leading to dV /dt = N sur + N em − N spin − N de in which N spin is the corresponding degrees of freedom related with the intrinsic spin of the matter content of the universe. Moreover, the validity of the unified first law and the generalized second law of thermodynamics for the Einstein-Cartan cosmos are investigated. Finally, by considering the covariant entropy conjecture and the bound resulting from the emergent scenario, a total entropy bound is obtained. Using this bound, it is shown that the for the universe as an expanding thermodynamical system, the total effective Komar energy never exceeds the square of the expansion rate with a factor of 3 4π .

We consider the Wheeler–DeWitt equation near the horizon of the black hole where the entangled vacuum state is chosen as the static universe state. Then, using the entangled property of the vacuum state, we investigate the dynamical evolution of the subsystems, namely inside and outside of the horizon

The cosmological candidate fields for dark energy as quintessence, phantom and cosmological constant are studied in terms of an entropic hypothesis imposed on the McVittie solution surrounded by dark energy. We certify this hypothesis as "D-bound-Bekenstein bound identification" for dilute systems and use it as a criterion to determine which candidate of dark energy can satisfy this criterion for a dilute McVittie solution. It turns out that only the cosmological constant can pass this criterion successfully while the quintessence and phantom fields fail, as non-viable dark energy fields for this particular black hole solution. Moreover, assuming this black hole to possess the saturated entropy, the entropy-area law and the holographic principle can put two constraints on the radius R of the cosmological horizon. The first one shows that the Hubble radius is discrete such that for any arbitrary value of the black hole mass m 0 , the value of R is determined up to an integer number. The latter one shows that when a black hole is immersed in a cosmological background, the radius of the cosmological horizon is constrained as R < 1 H .