The Thermodynamics of the Gravity from Entropy Theory

Abstract

The Gravity from Entropy (GfE) action posits that the fundamental nature of gravity is information encoded in the metric degrees of freedom. This statistical mechanics theory is associated with the GfE Lagrangian given by the Geometric Quantum Relative Entropy (GQRE) between the true metric and the metric induced by the matter fields and the curvature. The GfE action leads to the GfE modified gravity equations displaying an emergent dynamical cosmological constant. Interestingly, the GfE equations of motion reduce to the Einstein equations in the limit of low energy and small curvature. Here we embrace a thermodynamic point of view and we associate the energy density of the GfE to the emergent dynamical cosmological constant of the theory. Focusing on homogeneous and isotropic spacetimes, we reveal that the GfE universes associated with the FRW metrics are thermal. Indeed they are associated with the $k$-temperatures and the $k$-pressures which are related to their local GQRE and their local energy by the first law of GfE thermodynamics. The thermodynamics of the GfE theory is illustrated in the low energy, small curvature limit with matter content modelled as perfect fluid, where the solutions of the GfE equations of motion are well approximated by the Friedmann universes. We show that while the total GQRE per unit volume is not increasing, coherently with its relative entropy nature, the total entropy of GfE universes is not decreasing in time. These results provide a natural thermodynamic interpretation of GfE cosmologies and a framework for reconciling local complexity with the global increase in entropy of the universe.