Information content of spontaneous symmetry breaking

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, spatiallylocalized, 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.

Transition to order after hilltop inflation

“…As shown in Ref. [38], the RCE is extremely accurate when used to identify coherent configurations in nonlinear field models, showing a linear scaling with the number density of objects present. In Ref.…”

“…This quantity is initially negligible, and would remain constant under linear de Sitter expansion. Second, we use the relative configurational entropy (RCE) for the energy density [38], which provides an efficient quantitative measure for the presence of coherent classical field configurations in general nonlinear models [37]. (We have verified that both measures remain trivial for a particle rolling down an ordinary φ 4 potential without spontaneous symmetry breaking, in which case no oscillons form.)…”

“…As proposed in Ref. [38], the RCE is the field-theory equivalent of the Kullback-Leibler divergence of information theory, used there to discriminate between an arbitrary bit string and a fixed baseline or reference string [40], giving a probabilistic measure of the expected number of extra bits required to code samples of the desired string in terms of the baseline. In other words, the Kullback-Leibler divergence offers a "distance" in information complexity between the two strings.…”

“…In field theory, the RCE will give a "distance" in Fourier field configuration space between the measured fields and the baseline. In particular, following [38], we define the RCE in terms of a modal fraction f (k, t) computed from the energy density ρ(x, t),…”

Information content inF(R)brane models with nonconstant curvature

“…The approach presented in [22] has been used to study the non-equilibrium dynamics of spontaneous symmetry breaking [23], to obtain the stability bound for compact objects [24], to investigate the emergence of localized objects during inflationary preheating [25], and moreover, to distinguish configurations with energy-degenerate spatial profiles [26]. Furthermore, in a recent work [27], solitons, Lorentz symmetry breaking, supersymmetry, and entropy, were employed using the CE concept.…”