  We study the thermodynamic properties of high dimensional Schwarzschild de
Sitter spacetimes with the consideration of quantum effects. It is shown that
by considering the cosmological constant as a variable state parameter and
adding an extra term which denotes the vacuum energy, both the differential and
integral mass formulas of the first law of Schwarzschild de Sitter spacetimes
can be directly derived from the general Schwarzschild de Sitter metrics in a
simple and natural way. Furthermore, after taking quantum effects into account,
we can see that the cosmological constant must decrease and the spontaneous
decay of the vacuum energy never makes the entropy of Schwarzschild de Sitter
spacetimes decrease. In addition, though the laws of thermodynamics are very
powerful, at least the third law can not be applied to the Schwarzschild de
Sitter spacetimes. It should be emphasized that these conclusions come into
existence in any dimension.
