  In recent years, there has been significant interest in the field of extended
black hole thermodynamics, where the cosmological constant and/or other
coupling parameters are treated as thermodynamic variables. Drawing inspiration
from the Iyer-Wald formalism, which reveals the intrinsic and universal
structure of conventional black hole thermodynamics, we illustrate that a
proper extension of this formalism also unveils the underlying theoretical
structure of extended black hole thermodynamics. As a remarkable consequence,
for any gravitational theory described by a diffeomorphism invariant action, it
is always possible to construct a consistent extended thermodynamics using this
extended formalism.
