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

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.

5 pages, 2 PDF figures, uses RevTex4. v2: Modified the normalization condition in the entropy calculation to be more general and the figures were replaced to reflect that. Additional comments were added for clarity. v3: Minor rewordings, version to be published in Physics Letters B

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