According to GSLT, the entropy of horizon and entropy of matter resources inside horizon does not decrease with respect to time.
Next, we will discuss the various expressions of entropy-area relations in order analyze the validity of GSLT on Hubble horizon.
In order to analyze the clear picture of validity of GSLT for this entropy on the Hubble horizon, we plot [[??].sub.tot] against cosmic time (t) by fixing constant parameters as [alpha] = 0.2, [beta] = 0.00l, and n = 4 as shown in Figure 1.
In the following discussion we will analyze the validity of first law of thermodynamics with Gibbs relation, GSLT, and thermodynamical equilibrium by assuming the following entropy corrections.
We discuss the GSLT of an isolated macroscopic physical system where the total entropy [S.sub.T] must satisfy the following conditions d([S.sub.A] + [S.sub.f]) [greater than or equal to] 0; i.e., entropy function cannot be decreased.
Next, we observe the validity of GSLT by assuming Bekenstein entropy, logarithmic corrected entropy, power law correction, and Renyi entropy.
Using (15) and (16), the GSLT condition takes the form
It is seen that GSLT is valid for G > 0, F > 0 and [XI] > 0.
This result is analogous to the one presented in both [46, 47], though, in the former study, a mathematical condition was imposed to obtain similar restriction while, in the latter, it evolved through the validity of the GSLT. Further probing into the standard [LAMBDA]CDM model, we obtain [LAMBDA] = 3[H.sub.0.sup.2][[OMEGA].sub.[LAMBDA]].
A similar constraint was obtained assuming the validity of GSLT. The study remained to be model-independent and the positive brane tension did not play any crucial role for the attained result.
Therefore, GSLT is valid whenever we have[[??].sub.A]([rho] + p)/[[??].sub.A] + ([beta](t)/2)([??](t) + 3H[beta](t)) [greater than or equal to] 0.
meaning that GSLT is met when we have [[beta].sup.2] [greater than or equal to] (2[[??].sup.2.sub.A([rho] + p)/3)([??] - k/[a.sup.2]) yielding [[beta].sup.2] [greater than or equal to] 0 for a flat universe (k = 0) of constant Hubble parameter ([??] = 0).