  With the objective to generalize previous results found for a handful of
explicit solutions, we study the extended thermodynamics of a black brane with
minimally coupled scalar hair in D-dimensional asymptotically anti-de Sitter
spacetimes. Using Komar integration and the Hamiltonian formalism to calculate
the conserved charges, we obtain a Smarr relation that is applicable to a wide
variety of solutions and suggests a more general definition of the
thermodynamic volume. This volume is found to be proportional to the geometric
volume, and a simple prescription is given to calculate the constant of
proportionality. Moreover, the method of Hamiltonian perturbations yields an
extended first law of thermodynamics for hairy black branes, thus giving a
definition for their enthalpy. These results are then verified by applying them
to some of the explicit solutions that exist in the literature.
