  Based on the entropy relations, we derive thermodynamic bound for entropy and
area of horizons of Schwarzschild-dS black hole, including the event horizon,
Cauchy horizon and negative horizon (i.e. the horizon with negative value),
which are all geometrical bound and made up of the cosmological radius.
Consider the first derivative of entropy relations together, we get the first
law of thermodynamics for all horizons. We also obtain the Smarr relation of
horizons by using the scaling discussion. For thermodynamics of all horizons,
the cosmological constant is treated as a thermodynamical variable. Especially
for thermodynamics of negative horizon, it is defined well in the $r<0$ side of
spacetime. The validity of this formula seems to work well for three-horizons
black holes. We also generalize the discussion to thermodynamics for event
horizon and Cauchy horizon of Gauss-Bonnet charged flat black holes, as the
Gauss-Bonnet coupling constant is also considered as thermodynamical variable.
These give further clue on the crucial role that the entropy relations of
multi-horizons play in black hole thermodynamics and understanding the entropy
at the microscopic level.
