  We perform a general study of the thermodynamic properties of static
electrically charged black hole solutions of nonlinear electrodynamics
minimally coupled to gravitation in three space dimensions. The Lagrangian
densities governing the dynamics of these models in flat space are defined as
arbitrary functions of the gauge field invariants, constrained by some
requirements for physical admissibility. The exhaustive classification of these
theories in flat space, in terms of the behaviour of the Lagrangian densities
in vacuum and on the boundary of their domain of definition, defines twelve
families of admissible models. When these models are coupled to gravity, the
flat space classification leads to a complete characterization of the
associated sets of gravitating electrostatic spherically symmetric solutions by
their central and asymptotic behaviours. We focus on nine of these families,
which support asymptotically Schwarzschild-like black hole configurations, for
which the thermodynamic analysis is possible and pertinent. In this way, the
thermodynamic laws are extended to the sets of black hole solutions of these
families, for which the generic behaviours of the relevant state variables are
classified and thoroughly analyzed in terms of the aforementioned boundary
properties of the Lagrangians. Moreover, we find universal scaling laws (which
hold and are the same for all the black hole solutions of models belonging to
any of the nine families) running the thermodynamic variables with the electric
charge and the horizon radius. These scale transformations form a one-parameter
multiplicative group, leading to universal "renormalization group"-like
first-order differential equations. The beams of characteristics of these
equations generate the full set of black hole states associated to any of these
gravitating nonlinear electrodynamics...
