  In this paper we consider spacetimes in vacuum general relativity --possibly
coupled to a scalar field-- with a positive cosmological constant $\Lambda$. We
employ the Isolated Horizons (IH) formalism where the boundary conditions
imposed are that of two horizons, one of black hole type and the other, serving
as outer boundary, a cosmological horizon. As particular cases, we consider the
Schwarzschild-de Sitter spacetime, in both 2+1 and 3+1 dimensions. Within the
IH formalism, it is useful to define two different notions of energy for the
cosmological horizon, namely, the "mass" and the "energy". Empty de Sitter
space provides an striking example of such distinction: its horizon energy is
zero but the horizon mass takes a finite value given by $\pi/(2\sqrt\Lambda)$.
For both horizons we study their thermodynamic properties, compare our results
with those of Euclidean Hamiltonian methods and construct some generalized
Bekenstein entropy bounds. We discuss these new entropy bounds and compare them
with some recently proposed entropy bounds in the cosmological setting.
