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

Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA
Physics Letters B (Impact Factor: 6.02). 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.

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    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; · 6.02 Impact Factor
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    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).

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