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.
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