A non-equilibrium extension of quantum gravity

TL;DR

This paper extends quantum gravity path integral models to a non-equilibrium framework using a microcanonical ensemble, aiming to reconcile thermodynamic interpretations with solutions of Einstein's Equations that are out of equilibrium.

Contribution

It introduces a non-equilibrium extension of quantum gravity models by employing a microcanonical ensemble with constraints, contrasting the traditional equilibrium approach.

Findings

Proposes a non-equilibrium path integral formulation for quantum gravity.

Analyzes the relation between microcanonical and other statistical descriptions.

Discusses the consistency of the non-equilibrium model with general relativity.

Abstract

A variety of quantum gravity models (including spin foams) can be described using a path integral formulation. A path integral has a well-known statistical mechanical interpretation in connection with a canonical ensemble. In this sense, a path integral describes the thermodynamic equilibrium of a local system in a thermal bath. This interpretation is in contrast to solutions of Einstein's Equations which depart from local thermodynamical equilibrium (one example is shown explicitly). For this reason, we examine an extension of the path integral model to a (locally) non-equilibrium description. As a non-equilibrium description, we propose to use a global microcanonical ensemble with constraints. The constraints reduce the set of admissible microscopic states to be consistent with the macroscopic geometry. We also analyse the relation between the microcanonical description and a statistical approach not based on dynamical assumptions which has been proposed recently. This analysis is of interest for the test of consistency of the non-equilibrium description with general relativity and quantum field theory.