Thermodynamics of nonlinear electrodynamics black holes and the validity of weak cosmic censorship at charged particle absorption

We first use the Hamilton–Jacobi method to describe the motion in curved spacetime of a scalar particle and a fermion, which are shown to satisfy the same Hamilton–Jacobi equation. To investigate the laws of thermodynamics and the weak cosmic censorship, we focus on D-dimensional asymptotically AdS charged black hole solutions in general nonlinear electrodynamics (NLED). With absorbing a charged particle, the variation of the generic charged NLED black hole is calculated in the normal and extended phase spaces. In the normal phase space, where the cosmological constant and dimensionful parameters in NLED are fixed, the first and second laws of thermodynamics are satisfied. In the extended phase space, where the cosmological constant and dimensionful parameters in NLED are treated as thermodynamic variables, the first law of thermodynamics is also satisfied. However, the black hole entropy can either increase or decrease depending on the changes in the dimensionful parameters. Furthermore, we find that the weak cosmic censorship conjecture is valid for the extremal and near-extremal black holes in the both phase spaces.