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Abstract

In this work we derive general quantum phenomenological equations of
gravitational dynamics and analyse its features. The derivation uses the
formalism developed in thermodynamics of spacetime and introduces low energy
quantum gravity modifications to it. Quantum gravity effects are considered via
modification of Bekenstein entropy by an extra logarithmic term in the area.
This modification is predicted by several approaches to quantum gravity,
including loop quantum gravity, string theory, AdS/CFT correspondence and
generalised uncertainty principle phenomenology, giving our result a general
character. The derived equations generalise classical equations of motion of
unimodular gravity, instead of the ones of general relativity, and they contain
at most second derivatives of the metric. We provide two independent
derivations of the equations based on thermodynamics of local causal diamonds.
First one uses Jacobson's maximal vacuum entanglement hypothesis, the second
one Clausius entropy flux. Furthermore, we consider questions of diffeomorphism
and local Lorentz invariance of the resulting dynamics and discuss its
application to a simple cosmological model, finding a resolution of the
classical singularity.