  The present study is elaborated to investigate the validity of
thermodynamical laws in a modified teleparallel gravity based on higher-order
derivatives terms of torsion scalar. For this purpose, we consider spatially
flat FRW model filled with perfect fluid matter contents. Firstly, we explore
the possibility of existence of equilibrium as well as non-equilibrium picture
of thermodynamics in this extended version of teleprallel gravity. Here, we
present the first law and the generalized second law of thermodynamics (GSLT)
using Hubble horizon. It is found that non-equilibrium description of
thermodynamics exists in this theory with the presence of an extra term called
as entropy production term. We also establish GSLT using the logarithmic
corrected entropy. Further, by taking the equilibrium picture, we discuss
validity of GSLT at Hubble horizon for two $F$ different models. Using Gibbs
law and the assumption that temperature of matter within Hubble horizon is
similar to itself, we use different cases for choices scale factors to discuss
the GSLT validity graphically in all scenarios. It is found that the GSLT is
satisfied for a specified range of free parameters in all cases.
