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Abstract

The discovery of the various thermodynamical aspects of classical gravity has led to a picture in which Einstein equations might be seen as an equation of state, relating the dynamics of null hypersurfaces to thermodynamic relations for a system at or close to equilibrium. The explanation of such a fact is expected to come from a complete theory of quantum gravity. In absence of it, I will use a pregeometric model of emergent gravity to discuss the role of Wheeler's boundary of a boundary principle in this specific problem. The goal is to show the relevance of the equilibration of the microscopic degrees of freedom in establishing the thermodynamical status of the semiclassical gravity limit, and how the equilibration of the system might lead to additional physical effects. The role of phase transitions (conjectured in certain combinatorial models proposed to define a quantum theory of gravity, namely tensor models and group field theories) will be also considered in this light, showing how criticality and deviations from it relate to these ideas.