Thermodynamics as a framework for understanding gravitational dynamics and quantum gravity

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We present a review of concepts of thermodynamic of spacetime that allows for an understanding of the gravitational dynamics encoding in it, discussing also the recovery of Weyl transverse gravity instead of General Relativity. We also discuss how these tools can provide some hints in the search of quantum gravity phenomenology, by introducing a formalism to analyze low-energy quantum gravity modifications in a completely general framework based on the thermodynamics of spacetime. For that purpose, we consider quantum gravity effects via a parametrized modification of entropy by an extra logarithmic term in the area, predicted in most of the different approaches to quantum gravity. These results provide a general expression for quantum phenomenological equations of gravitational dynamics.