Article

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

Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA
(Impact Factor: 6.13). 11/2011; 713(3). DOI: 10.1016/j.physletb.2012.05.064
Source: arXiv

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.

### Full-text

Available from: Marcelo Gleiser, Oct 02, 2015
0 Followers
·
• Source
##### Article: Information Content of Spontaneous Symmetry Breaking
[Hide abstract]
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.
Physical review D: Particles and fields 05/2012; 86(4). DOI:10.1103/PhysRevD.86.045004 · 4.86 Impact Factor
• Source
##### Article: Information-Entropic Stability Bound for Compact Objects: Application to Q-Balls and the Chandrasekhar Limit of Polytropes
[Hide abstract]
ABSTRACT: Spatially-bound objects across diverse length and energy scales are characterized by a binding energy. We propose that their spatial structure is mathematically encoded as information in their momentum modes and described by a measure known as configurational entropy (CE). Investigating solitonic Q-balls and stars with a polytropic equation of state $P = K{\rho}^{\gamma}$, we show that objects with large binding energy have low CE, whereas those at the brink of instability (zero binding energy) have near maximal CE. In particular, we use the CE to find the critical charge allowing for classically stable Q-balls and the Chandrasekhar limit for white dwarfs $({\gamma} = 4/3)$ with an accuracy of a few percent.
Physics Letters B 07/2013; 727(1-3). DOI:10.1016/j.physletb.2013.10.005 · 6.13 Impact Factor
• Source
##### Article: Transition To Order After Hilltop Inflation
[Hide abstract]
ABSTRACT: We investigate the rich nonlinear dynamics during the end of hilltop inflation by numerically solving the coupled Klein-Gordon-Friedmann equations in a expanding universe. In particular, we search for coherent, nonperturbative configurations that may emerge due to the combination of nontrivial couplings between the fields and resonant effects from the cosmological expansion. We couple a massless field to the inflaton to investigate its effect on the existence and stability of coherent configurations and the effective equation of state at reheating. For parameters consistent with data from the Planck and WMAP satellites, and for a wide range of couplings between the inflaton and the massless field, we identify a transition from disorder to order characterized by emergent oscillon-like configurations. We verify that these configurations can contribute a maximum of roughly 30% of the energy density in the universe. At late times their contribution to the energy density drops to about 3%, but they remain long-lived on cosmological time-scales, being stable throughout our simulations. Cosmological oscillon emergence is described using a new measure of order in field theory known as relative configurational entropy.
Physical Review D 01/2014; 89(8). DOI:10.1103/PhysRevD.89.083502 · 4.64 Impact Factor