# Generalized Gibbs Ensembles in Discrete Quantum Gravity

## TL;DR

This paper extends the concept of Gibbs states to discrete quantum gravity, proposing a covariant statistical framework for spacetime emergence using information theory and quantum geometry models.

## Contribution

It introduces a generalized Gibbs state approach to quantum gravity, linking statistical mechanics with quantum geometry and spacetime emergence.

## Key findings

- Gibbs state description of tetrahedral geometry in quantum gravity
- Effective statistical field theory for generating discrete spacetime histories
- Application of information-theoretic concepts to quantum gravity

## Abstract

Maximum entropy principle and Souriau's symplectic generalization of Gibbs states have provided crucial insights leading to extensions of standard equilibrium statistical mechanics and thermodynamics. In this brief contribution, we show how such extensions are instrumental in the setting of discrete quantum gravity, towards providing a covariant statistical framework for the emergence of continuum spacetime. We discuss the significant role played by information-theoretic characterizations of equilibrium. We present the Gibbs state description of the geometry of a tetrahedron and its quantization, thereby providing a statistical description of the characterizing quanta of space in quantum gravity. We use field coherent states for a generalized Gibbs state to write an effective statistical field theory that perturbatively generates 2-complexes, which are discrete spacetime histories in several quantum gravity approaches.