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

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

2004-02-25

arxiv.org/abs/cond-mat/0402635v2

Eur. Phys. J. B 52, 113-117 (2006)

Physics

Condensed Matter

Statistical Mechanics

New title, revision of the text. EPJ latex, 4 figures

Scientific paper

10.1140/epjb/e2006-00265-y

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.

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