Thermodynamics in $f(T)$ Gravity and Corrected Entropies

This paper is devoted to study the generalized second law of thermodynamics in $f(T)$ gravity. We use quantum corrections such as power-law and logarithmic corrected entropies to the horizon entropy along with Gibbs' equation in the thermal equilibrium state. We derive $f(T)$ model by taking into account a power-law scale factor through the first modified Friedmann equation which obeys the condition for a realistic model. Two types of horizons, i.e., Hubble and event horizons are used to check the validity of the generalized second law of thermodynamics with corrected entropies. We conclude that this law holds with a specific range of entropy parameter on both horizons in the case of power-law corrected entropy, while it violates for all values of entropy parameter on both horizons for logarithmic corrected entropy.