  In this work we study a homogeneous and quasilocal Thermodynamics associated
to the Schwarzschild-anti de Sitter black hole. The usual thermodynamic
description is extended within a Hamiltonian approach with the introduction of
the cosmological constant in the thermodynamic phase space. The treatment
presented is consistent in as much as it respects the laws of black hole
Thermodynamics and accepts the introduction of any thermodynamic potential. We
are able to construct new equations of state that characterize the
Thermodynamics. Novel phenomena can be expected from the proposed setup.
