  We implement a general numerical calculation that allows for a direct
comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs
canonical distribution in Gibbs $\Gamma$-space. Using paradigmatic
first-neighbor models, namely, the inertial XY ferromagnet and the
Fermi-Pasta-Ulam $\beta$-model, we show that at intermediate energies the
Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law
(${\mathbf F}=m{\mathbf a}$). At higher energies we discuss partial agreement
between time and ensemble averages.
