Physics Letters B 790 (2019) 197–204
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Physics Letters B
www.elsevier.com/locate/physletb
Configurational entropy of tachyon kinks on unstable Dp-branes
Chong Oh Lee
Department of Physics, Kunsan National University, Kunsan 573-701, Republic of Korea
a r t i c l e i n f o a b s t r a c t
Article history:
Received
17 December 2018
Received
in revised form 14 January 2019
Accepted
16 January 2019
Available
online 22 January 2019
Editor:
M. Cveti
ˇ
c
We consider tachyon effective theory with Born–Infeld electromagnetic fields and investigate the
configurational entropy of the various tachyon kink solutions. We find that the configurational entropy
starts at a minimum value and saturates to a maximum value as the negative pressure of pure tachyonic
field increases. In particular, when an electric field is turned on and its magnitude is larger than or equal
to the critical value, we find the configurational entropy has a global minimum, which is related to the
predominant tachyonic states.
© 2019 The Author(s). 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
The investigation of a D-brane with tachyon condensation [1]
has
opened up a new window to explore off-shell structure of
string theory. It was found that rolling tachyon solutions through
boundary conformal field theory and effective field theory de-
scribe
the motion of the tachyon on unstable D-branes [2–4]. It
was extensively studied for the inhomogeneous tachyon condensa-
tion [5–8],
the emission of closed string radiation [9,10] and for
instability of codimension-one D-branes [9,11–13].
It
was found that the configurational entropy represents the
informational content in physical systems with localized energy
density configurations through measure of their ordering in field
configuration space [14,15]. It was extensively studied for AdS/QCD
holographic models [16–22] and for instability of a variety of
physical systems [15–17,23–29]. In particular, the configurational
entropy was investigated for dynamical tachyonic AdS/QCD holo-
graphic
model. The authors showed that the corrections to dual
mesonic states in the boundary QCD due to tachyonic fields be-
come
more dominant their states [19]. Since decay of unstable
D-branes has rich tachyon kink solutions, it is intriguing to cal-
culate
the configurational entropy of tachyon kink solutions.
The
paper is organized as follows: in the next section we will
investigate configurational entropy in tachyon effective theory with
Born–Infeld electromagnetic fields. Firstly, we will calculate the
configurational entropy in the pure tachyon case. Next, we will
turn on electric/electromagnetic field. Then the configurational en-
tropy
will be computed. We will also discuss their configurational
E-mail address: cohlee@gmail.com.
entropy by varying the electromagnetic field. In the last section we
will give our conclusion.
2. Configurational entropy of tachyon kinks
The Boltzmann–Gibbs entropy S
BG
is defined as
S
BG
=−k
B
p
i
ln p
i
, (2.1)
with
p
i
= 1. In fact, it is given as the most general formula be-
tween
the entropy and the set of probabilities of their microscopic
states in statistical thermodynamics. Here, k
B
is the Boltzmann
constant, and p
i
the probability of a microstate, respectively. In
particular, when each microstate has equal probability as the fol-
lowing
p
i
=
1
W
, (2.2)
with the number of microstates W , S
BG
(2.1)reduces to the con-
figurational
entropy S
C
in the microcanonical ensemble
S
C
=k
B
ln W , (2.3)
since W can be treated as the number of possible configurations
at a given energy. For example, there are two different molecules
with the total number of molecules N
0
, then the number of
one type of molecule is N
1
and the number of another type of
molecule N
2
. One obtains the configurational entropy S
C
S
C
=k
B
ln W =k
B
ln
N
0
!
N
1
!N
2
!
,
(2.4)
and after employing Sterling’s approximation ln N! ≈ N ln N, one
has
https://doi.org/10.1016/j.physletb.2019.01.026
0370-2693/
© 2019 The Author(s). 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
.