Thermodynamics and weak cosmic censorship conjecture of the BTZ black holes in the extended phase space

As charged fermions drop into the BTZ black holes, we check the laws of thermodynamics and weak cosmic censorship conjecture in the normal phase space and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics as well as the weak cosmic censorship are valid. While in the extended phase space, though the first law and weakcosmic censorship conjecture are still valid, the second law is dependent on the variation of the renormalization energy $dK$. In addition, in the extended phase space, the configurations of the extremal and near-extremal black holes will not be changed for they are stable while in the normal phase space, the extremal and near-extremal black holes will evolve into non-extremal black holes.