  As the interaction between the black holes and highly energetic infalling
charged matter receives quantum corrections, the basic laws of black hole
mechanics have to be carefully rederived. Using the covariant phase space
formalism, we generalize the first law of black hole mechanics, both
"equilibrium state" and "physical process" versions, in the presence of
nonlinear electrodynamics fields, defined by Lagrangians depending on both
quadratic electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star
F}^{ab}$. Derivation of this law demands a specific treatment of the Lagrangian
parameters, similar to embedding of the cosmological constant into
thermodynamic context. Furthermore, we discuss the validity of energy
conditions, several complementing proofs of the zeroth law of black hole
electrodynamics and some aspects of the recently generalized Smarr formula, its
(non-)linearity and relation to the first law.
