Information Content of Spontaneous Symmetry Breaking

TL;DR

This paper introduces a new measure called relative configurational entropy (RCE) to quantify the emergence of structured, low-entropy configurations like oscillons during spontaneous symmetry-breaking in nonequilibrium field dynamics.

Contribution

It proposes RCE as a novel quantitative tool to analyze the formation of coherent structures in nonequilibrium systems, demonstrated through scalar field simulations.

Findings

RCE correlates with oscillon number density

Oscillons emerge during symmetry-breaking at specific initial temperatures

RCE effectively quantifies nonperturbative spatiotemporal patterns

Abstract

We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially-extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry-breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially-localized, long-lived structures known as oscillons emerge in synchrony and remain until the field reaches equilibrium again. We show that the RCE correlates with the number-density of oscillons, thus offering a quantitative measure of the emergence of nonperturbative spatiotemporal patterns that can be generalized to a variety of physical systems.