Entropic Measure for Localized Energy Configurations: Kinks, Bounces, and Bubbles

TL;DR

This paper introduces a configurational entropy measure in functional space to analyze localized energy solutions in scalar field models, providing a new way to compare and select solutions based on informational content.

Contribution

It develops a novel configurational entropy measure applicable to scalar field solutions with localized energy, linking energy approximation quality to entropy and aiding solution selection.

Findings

Higher energy trial functions have higher relative configurational entropy.

Configurational entropy can distinguish between degenerate energy solutions.

The measure connects dynamical properties with informational content in physical models.

Abstract

We construct a configurational entropy measure in functional space. We apply it to several nonlinear scalar field models featuring solutions with spatially-localized energy, including solitons and bounces in one spatial dimension, and critical bubbles in three spatial dimensions, typical of first-order phase transitions. Such field models are of widespread interest in many areas of physics, from high energy and cosmology to condensed matter. Using a variational approach, we show that the higher the energy of a trial function that approximates the actual solution, the higher its relative configurational entropy, defined as the absolute difference between the configurational entropy of the actual solution and of the trial function. Furthermore, we show that when different trial functions have degenerate energies, the configurational entropy can be used to select the best fit to the actual solution. The configurational entropy relates the dynamical and informational content of physical models with localized energy configurations.