Generalized second law of thermodynamics in<i>f</i>(<i>T</i>) gravity

We investigate the validity of the generalized second law (GSL) of gravitational thermodynamics in the framework of f(T) modified teleparallel gravity. We consider a spatially flat FRW universe containing only the pressureless matter. The boundary of the universe is assumed to be enclosed by the Hubble horizon. For two viable f(T) models containing $f(T)=T+\mu_1{(-T)}^n$ and $f(T)=T-\mu_2 T(1-e^{\beta\frac{T_0}{T}})$, we first calculate the effective equation of state and deceleration parameters. Then, we investigate the null and strong energy conditions and conclude that a sudden future singularity appears in both models. Furthermore, using a cosmographic analysis we check the viability of two models. Finally, we examine the validity of the GSL and find that for both models it is satisfied from the early times to the present epoch. But in the future, the GSL is violated for the special ranges of the torsion scalar T.