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 [34]

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 [8]

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 [22]

From this equation we can define the

apparent horizon as follows: