  We discuss the form of the entropy for classical hamiltonian systems with
long-range interaction using the Vlasov equation which describes the dynamics
of a $N$-particle in the limit $N\to\infty$. The stationary states of the
hamiltonian system are subject to infinite conserved quantities due to the
Vlasov dynamics. We show that the stationary states correspond to an extremum
of the Boltzmann-Gibbs entropy, and their stability is obtained from the
condition that this extremum is a maximum. As a consequence the entropy is a
function of an infinite set of Lagrange multipliers that depend on the initial
condition. We also discuss in this context the meaning of ensemble
inequivalence and the temperature.
