This shows that [[??].sub.tot] remains positive with increasing value of t which confirms the validity of GSLT at apparent horizon
with Bekenstein entropy.
According to the assumptions above, the boundary maybe decomposed into future (+) and past (-) apparent horizon
components [partial derivative]M = [[partial derivative].sub.+]M [union] [[partial derivative].sub.-] M.
(i) Bekenstein entropy: the Bekenstein entropy and Hawking temperature of the apparent horizon
are given by (8[pi] = G = 1)
Cai, "Thermodynamical properties of apparent horizon
in warped DGP braneworld," Nuclear Physics B, vol.
In this section, we study the laws of thermodynamics in the context of f(G, T) gravity at the apparent horizon
of FRW universe model.
We note that, based on spacetime thermodynamics, a proper causal boundary of the classical spacetime is its apparent horizon
[45, 46], meaning that the metric fluctuations are bounded by [R.sub.H] and also that thermodynamics laws are satisfied on this boundary [47, 48].
Moreover, the volume (V) and the area (A) of the apparent horizon
of an n-sphere with radius [r.sub.A] satisfy 
In Section 2, we reviewed the cosmical apparent horizon
and derived the holographic-style dynamical equations in the EBI theory.
For an energy-momentum source with [T.sup.b.sub.a] = diag(-[rho], p, p, p), the amount of energy crossing the apparent horizon
is evaluated as 
Due to the effect of rainbow gravity, the deformed Friedmann equation (44) becomes susceptible when the apparent horizon
approaches the order of Planck scale.
Now we investigate the thermodynamic behavior of the nonminimal f(T) gravity on the apparent horizon
. In the flat FRW universe, the radius [[??].sub.A] of the dynamical apparent horizon
is given by 
From this equation we can define the apparent horizon