Physics Letters B 755 (2016) 358–362
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Bounds on topological Abelian string-vortex and string-cigar from
information-entropic measure
R.A.C. Correa
a
, D.M. Dantas
b
, C.A.S. Almeida
c
, Roldão da Rocha
d,∗
a
CCNH, Universidade Federal do ABC (UFABC), 09210-580, Santo André, SP, Brazil
b
Universidade Federal do Ceará (UFC), 60455-760, Fortaleza, CE, Brazil
c
Universidade Federal do Ceará (UFC), Departamento de Física, 60455-760, Fortaleza, CE, Brazil
d
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), 09210-580, Santo André, SP, Brazil
a r t i c l e i n f o a b s t r a c t
Article history:
Received
30 December 2015
Received
in revised form 17 February 2016
Accepted
17 February 2016
Available
online 23 February 2016
Editor:
N. Lambert
Keywords:
Topological
Abelian string-vortex
Six-dimensional
braneworld models
Configurational
entropy
In this work we obtain bounds on the topological Abelian string-vortex and on the string-cigar, by
using a new measure of configurational complexity, known as configurational entropy. In this way, the
information-theoretical measure of six-dimensional braneworlds scenarios is capable to probe situations
where the parameters responsible for the brane thickness are arbitrary. The so-called configurational
entropy (CE) selects the best value of the parameter in the model. This is accomplished by minimizing
the CE, namely, by selecting the most appropriate parameters in the model that correspond to the most
organized system, based upon the Shannon information theory. This information-theoretical measure of
complexity provides a complementary perspective to situations where strictly energy-based arguments
are inconclusive. We show that the higher the energy the higher the CE, what shows an important
correlation between the energy of the a localized field configuration and its associated entropic measure.
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
In 1948, in a seminal work, Shannon [1] introduced the infor-
mation
theory, whose main goal was to introduce the concepts of
entropy and mutual information, using the communication theory.
Therein, the entropy was defined to be a measure of “randomness”
of a random phenomenon. Thus, if a little deal of information con-
cerning
a random variable is received, the uncertainty decreases,
which makes it possible to measure the decrement in the uncer-
tainty,
related to the quantity of transmitted information. Inspired
by Shannon, Gleiser and Stamatopoulos (GS) latterly introduced a
measure of complexity of a localized mathematical function [2]. GS
proposed that the Fourier modes of square-integrable, bounded,
mathematical functions can be used to construct a measure, the
so-called configurational entropy (CE). A single mode system has
zero CE, whereas that one where all modes contribute with equal
weight has maximal CE. In order to apply such ideas to physical
models, GS used the energy density of a given spatially-localized
*
Corresponding author.
E-mail
addresses: rafael.couceiro@ufabc.edu.br (R.A.C. Correa), davi@fisica.ufc.br
(D.M. Dantas),
carlos@fisica.ufc.br (C.A.S. Almeida), roldao.rocha@ufabc.edu.br
(R. da Rocha).
field configuration, as a solution of the related partial differential
equation (PDE). Hence the CE can be used to choose the best fit-
ting
trial function with energy degeneracy.
The
CE has been already employed to acquire the stability
bound for compact objects [3], to investigate the non-equilibrium
dynamics of spontaneous symmetry breaking [4], to study the
emergence of localized objects during inflationary preheating [5]
and
to discern configurations with degenerate-energy spatial pro-
files
[6]. Moreover, solitons were studied in a Lorentz symmetry
violating (LV) framework with the aid of CE [7–10]. In this con-
text,
the CE associated to travelling solitons in LV frameworks plays
a prominent role in probing systems wherein the parameters are
somehow arbitrary. Furthermore, the CE identifies critical points in
continuous phase transitions [11]. Moreover, the CE can be used
to measure the informational organization in the structure of the
system configuration for five-dimensional (5D) thick scenarios. In
particular, the CE plays an important role to decide the most ap-
propriate
intrinsic parameters of sine-Gordon braneworld models
[12], being further studied both in f (R) [13] and f (R, T ) [14] the-
ories
of gravity. In what follows, we present a brief discussion of
5D braneworld models to treat the CE in six-dimensional (6D) sce-
narios.
Randall–Sundrum
(RS) models [15,16] proposed a warped
braneworld scenario, wherein the gauge hierarchy problem is
http://dx.doi.org/10.1016/j.physletb.2016.02.038
0370-2693/
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.