Thermodynamics of spherically symmetric black holes in scale-dependent gravity

In this work we extend the first law of thermodynamics to spherically symmetric black hole solutions in the context of scale-dependent gravity. After deriving generalized expressions for both the entropy and energy due to the spatial variation of the gravitational constant we analize, by pointing out some relations between scale-dependent and f ( R ) theories, whether or not the former can be described using equilibrium thermodynamics.