Considering corrections produced by modified dispersion relations on the equation of state parameter of radiation, we study the induced black hole metric inspired by Kiselevs ansatz, thus defining a deformed Reissner-Nordstr{o}m metric. In particular
, we consider thermodynamic properties of such a black hole from the combined viewpoints of the modified equation of state parameter and the phenomenological approach to the quantum gravity problem called rainbow gravity.
We study some properties of the extended phase space of a quantum-corrected Schwarzschild black hole surrounded by a perfect fluid. In particular we demonstrate that, due to the quantum correction, there exist first and second order phase transitions
for a certain range of the state parameter of the perfect fluid, and we explicitly analyze some cases. Besides that, we describe the efficiency of this system as a heat engine and the effect of quantum corrections for different surrounding fluids.
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.
