It is argued that Planck mass may be considered as a candidate for the mass content of degrees of freedom of holographic screen. In addition, employing the Verlinde hypothesis on emergent gravity and considering holographic screen degrees of freedom
as a $q$-deformed fermionic system, it is obtained that the heat capacity per degree of freedom inspires the MOND interpolating function. Moreover, the MOND acceleration is achieved as a function of Planck acceleration. Both ultra-relativistic and non-relativistic statistics are studied.
We study some cosmological features of Tsallis holographic dark energy (THDE) in Cyclic, DGP and RS II braneworlds. In our setup, a flat FRW universe is considered filled by a pressureless source and THDE with the Hubble radius as the IR cutoff, whil
e there is no interaction between them. Our result shows that although suitable behavior can be obtained for the system parameters such as the deceleration parameter, the models are not always stable during the cosmic evolution at the classical level.
Accepting the Komar mass definition of a source with energy-momentum tensor $T_{mu u}$, and using the thermodynamic pressure definition, we find a relaxed energy-momentum conservation law. Thereinafter, we study some cosmological consequences of the
obtained energy-momentum conservation law. It has been found out that the dark sectors of cosmos are unifiable into one cosmic fluid in our setup. While this cosmic fluid impels the universe to enter an accelerated expansion phase, it may even show a baryonic behavior by itself during the cosmos evolution. Indeed, in this manner, while $T_{mu u}$ behaves baryonically, some parts of it, namely $T_{mu u}(e)$ which is satisfying the ordinary energy-momentum conservation law, are responsible for the current accelerated expansion.
Using the Tsallis generalized entropy, holographic hypothesis and also considering the Hubble horizon as the IR cutoff, we build a holographic model for dark energy and study its cosmological consequences in the Brans-Dicke framework. At first, we fo
cus on a non-interacting universe, and thereinafter, we study the results of considering a sign-changeable interaction between the dark sectors of the cosmos. Our investigations show that, compared with the flat case, the power and freedom of the model in describing the cosmic evolution is significantly increased in the presence of the curvature. The stability analysis also indicates that, independent of the universe curvature, both the interacting and non-interacting cases are classically unstable. In fact, both the classical stability criterion and an acceptable behavior for the cosmos quantities, including the deceleration and density parameters as well as the equation of state, are not simultaneously obtainable.
