Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: a computational discussion

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs iota-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 (F=ma). At higher energies we discuss partial agreement between time and ensemble averages.