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In this work, the role of a time-varying Newton constant under the scale-dependent approach is investigated in the thermodynamics of the Friedman equations. In particular, we show that the extended Friedman equations can be derived either from equilibrium thermodynamics when the non-matter energy momentum tensor is interpreted as a fluid or from non-equilibrium thermodynamics when an entropy production term, which depends on the time-varying Newton constant, is included. Finally, a comparison between black hole and cosmological thermodynamics in the framework of scale--dependent gravity is briefly discussed.
With the help of a masslike function which has dimension of energy and equals to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon $dE=T_AdS_A$ can be derived from the Friedmann equati
We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We app
We study photon orbits in the background of $(1+3)$-dimensional static, spherically symmetric geometries. In particular, we have obtained exact analytical solutions to the null geodesic equations for light rays in terms of the Weierstra{ss} function
We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eotvos. This new degree of freedom allows for evolving gravitati
We consider spatially homogeneous and isotropic cosmologies with non-zero torsion. Given the high symmetry of these universes, we adopt a specific form for the torsion tensor that preserves the homogeneity and isotropy of the spatial surfaces. Employ