  In a generic theory of gravity coupled to matter fields, the Smarr formula
for black holes does not work properly if the contributions of the coupling
constants defining the theory are not incorporated. However, these couplings,
such as the cosmological constant or the dimensionful parameters that appear in
the Lagrangian, are fixed parameters defining the theory, and they cannot be
varied. Here, we present a robust method, applicable to any covariant
Lagrangian, that upgrades the role of the couplings from being constants in the
theory to being free parameters of the solutions. To this end, for each one of
the couplings in a theory, a pair of auxiliary scalar and gauge fields is
introduced. The couplings are shown to be conserved charges of the global part
of the implemented gauge symmetry. Besides, their conjugate chemical potentials
are defined as the electric potential of the corresponding gauge fields on the
black hole horizon. Using this method, we systematically extend the first law
and the Smarr formula by coupling conserved charges and their conjugate
potentials. The thermodynamics of a black hole solution in a quadratic gravity
theory is given as an example.
