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

Fulvio Baldovin·Luis G. Moyano·Constantino Tsallis
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Abstract

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $Γ$-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam $β$-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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Fulvio Baldovin, Luis G. Moyano, Constantino Tsallis. 2006-08-28. Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: A computational discussion. https://doi.org/10.1140/epjb%2Fe2006-00265-y

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