The Entropy of the Gravitational Field

TL;DR

This paper develops a formalism to calculate the nonequilibrium entropy of gravitational fields using correlation functions, and applies it to cosmological models, revealing entropy levels surpassing microwave background fluctuations.

Contribution

It introduces a new correlation-function-based formula for gravitational entropy and applies it to inflationary cosmology, providing insights into entropy evolution in the early universe.

Findings

Entropy in density perturbations exceeds microwave background fluctuations.

The formalism links gravitational entropy to correlation functions.

Entropy increases during inflationary expansion.

Abstract

We derive a formula for the nonequilibrium entropy of a classical stochastic field in terms of correlation functions of this field. The formalism is then applied to define the entropy of gravitational perturbations (both gravitational waves and density fluctuations). We calculate this entropy in a specific cosmological model (the inflationary Universe) and find that on scales of interest in cosmology the entropy in both density perturbations and gravitational waves exceeds the entropy of statistical fluctuations of the microwave background. The nonequilibrium entropy discussed here is a measure of loss of information about the system. We discuss the origin of the entropy in our cosmological models and compare the definition of entropy in terms of correlation functions with the microcanonical definition in quantum statistical mechanics.