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Abstract
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Based on Padmanabhan’s proposal, the acceler-
ated expansion of the universe can be driven by the difference
between the surface and bulk degrees of freedom in a region
of space, described by the relation d
V
/
d
t
=
N
sur
−
N
bulk
where
N
sur
and
N
bulk
=−
N
em
+
N
de
are the degrees of
freedom assigned to the surface area and the matter–energy
content inside the bulk such that the indices “em” and “de”
represent energy-momentum and dark energy, respectively.
In the present work, the dynamical effect of the Weyssen-
hoff perfect fluid with intrinsic spin and its corresponding
spin degrees of freedom in the framework of Einstein–Cartan
(EC) theory are investigated. Based on the modification of
Friedmann equations due to the spin–spin interactions, a cor-
rection term for Padmanabhan’s original relation d
V
/
d
t
=
N
sur
+
N
em
−
N
de
including the number of degrees of freedom
related with these spin interactions is obtained through the
modification in
N
bulk
term as
N
bulk
=−
N
em
+
N
spin
+
N
de
leading to d
V
/
d
t
=
N
sur
+
N
em
−
N
spin
−
N
de
in which
N
spin
is the corresponding degrees of freedom related with the
intrinsic spin of the matter content of the universe. Moreover,
the validity of the unified first law and the generalized second
law of thermodynamics for the Einstein–Cartan cosmos are
investigated. Finally, by considering the covariant entropy
conjecture and the bound resulting from the emergent sce-
nario, a total entropy bound is obtained. Using this bound,
it is shown that the for the universe as an expanding ther-
modynamical system, the total effective Komar energy never
exceeds the square of the expansion rate with a factor of
3
4
π
.
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