  The activation temperature $T$ in the de Sitter environment is twice larger
than the Gibbons-Hawking temperature, related to the cosmological horizon. We
consider the activation temperature as the local temperature of the de Sitter
vacuum, and construct the local thermodynamics of the de Sitter state. This
thermodynamics includes also the gravitational coupling $K$ and the scalar
Riemann curvature ${\cal R}$ as the thermodynamically conjugate variables.
These variables modify the thermodynamics of the Gibbs-Duhem relation in the de
Sitter state. The free energy density is proportional to $-T^2$, which is
similar to that in the non-relativistic Fermi liquids and in relativistic
matter with equation of state $w=1$. The local entropy is proportional to the
local temperature, while the total entropy inside the cosmological horizon is
$A/4G$, where $A$ is the area of the horizon. This entropy is usually
interpreted as the entropy of the cosmological horizon. We also consider the
possible application of the de Sitter thermodynamics to the Schwarzschild-de
Sitter black hole and to black and white holes with the de Sitter cores.
