Research Article
Irreversible Thermodynamics of the Universe:
Constraints from Planck Data
Subhajit Saha,
1
Atreyee Biswas,
2
and Subenoy Chakraborty
1
1
Department of Mathematics, Jadavpur University, Kolkata, West Bengal 700032, India
2
Department of Natural Sciences, West Bengal University of Technology, BF 142, Sector 1, Salt Lake, Kolkata,
West Bengal 700064, India
Correspondence should be addressed to Subhajit Saha; subhajit1729@gmail.com
Received 22 September 2014; Accepted 14 November 2014; Published 4 December 2014
Academic Editor: Elias C. Vagenas
Copyright © 2014 Subhajit Saha et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e
publication of this article was funded by SCOAP
3
.
e present work deals with irreversible universal thermodynamics. e homogenous and isotropic at model of the universe
is chosen as open thermodynamical system and nonequilibrium thermodynamics comes into picture. For simplicity, entropy
ow is considered only due to heat conduction. Further, due to Maxwell-Cattaneo modied Fourier law for nonequilibrium
phenomenon, the temperature satises damped wave equation instead of heat conduction equation. Validity of generalized second
law of thermodynamics (GSLT) has been investigated for universe bounded by apparent or event horizon with cosmic substratum
as perfect uid with constant or variable equation of state or interacting dark species. Finally, we have used three Planck data sets to
constrain the thermal conductivity and the coupling parameter
2
. ese constraints must be satised in order for GSLT to hold
for universe bounded by apparent or event horizons.
1. Introduction
is is now well established that there is a profound relation
between gravity and thermodynamics. In the 1970s Hawking
[1]andBekenstein[2]gaverisetothisuniqueideawith
their revolutionary discovery of black hole thermodynamics.
According to them, black hole behaves as a black body
whose temperature (known as Hawking temperature) and
entropy (known as Bekenstein entropy) are proportional to
the surface gravity at the horizon and area of the horizon,
respectively. Later Bardeen et al. [3], in 1973, established that
thefourlawsofblackholemechanicsareactuallyanalo-
gous to four laws of thermodynamics. As thermodynamical
parameters such as temperature and entropy are character-
ized by the geometry of the event horizon of the black hole,
it is legitimated to assume that black hole thermodynamics
is deeply related to Einstein’s eld equations. is assertion
became true when Jacobson [4] in 1995 successfully derived
Einstein equation from the rst law of thermodynamics,
= with and as the energy ux and Unruh
temperaturemeasuredbyanacceleratedobserverjustinside
the horizon, and subsequently Padmanabhan [5] derived the
rst law of thermodynamics from Einstein equations for
general static spherically symmetric space time. Since then,
much work has been done based on this equivalence between
Einstein’s equations and thermodynamics.
Universal thermodynamics got a new direction when it
was understood that the universe should be an irreversible
one rather than a reversible one [6, 7]. Jacobson [4]rst
noticedthiswhenhisattemptfailedtoreproduceEinstein’s
equations from rst law of thermodynamics in ()gravity.
In that case he assumed the horizon entropy to be pro-
portional to a function of the Ricci scalar and this led to
the breakdown of the local thermodynamical equilibrium.
Subsequently, Eling et al. [6, 7]hadshownthat,byacurvature
correction to the entropy which is polynomial in the Ricci
scalar, Einstein’s equations can be derived from thermody-
namic laws in ()gravity by a nonequilibrium treatment.
Hindawi Publishing Corporation
Advances in High Energy Physics
Volume 2014, Article ID 652962, 9 pages
http://dx.doi.org/10.1155/2014/652962