  We consider a static self-gravitating perfect fluid system in Lovelock
gravity theory. For a spacial region on the hypersurface orthogonal to static
Killing vector, by the Tolman's law of temperature, the assumption of a fixed
total particle number inside the spacial region, and all of the variations (of
relevant fields) in which the induced metric and its first derivatives are
fixed on the boundary of the spacial region, then with the help of the
gravitational equations of the theory, we can prove a theorem says that the
total entropy of the fluid in this region takes an extremum value. A converse
theorem can also be obtained following the reverse process of our proof. We
also propose the definition of isolation quasi-locally for the system and
explain the physical meaning of the boundary conditions in the proof of the
theorems.
