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arXiv · 1003.5495

Thermostatistics in the neighborhood of the $π$-mode solution for the Fermi-Pasta-Ulam $β$ system: from weak to strong chaos

M. Leo·R. A. Leo·P. Tempesta
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Abstract

We consider a $π$-mode solution of the Fermi-Pasta-Ulam $β$ system. By perturbing it, we study the system as a function of the energy density from a regime where the solution is stable to a regime, where is unstable, first weakly and then strongly chaotic. We introduce, as indicator of stochasticity, the ratio $ρ$ (when is defined) between the second and the first moment of a given probability distribution. We will show numerically that the transition between weak and strong chaos can be interpreted as the symmetry breaking of a set of suitable dynamical variables. Moreover, we show that in the region of weak chaos there is numerical evidence that the thermostatistic is governed by the Tsallis distribution.

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M. Leo, R. A. Leo, P. Tempesta. 2010-03-29. Thermostatistics in the neighborhood of the $π$-mode solution for the Fermi-Pasta-Ulam $β$ system: from weak to strong chaos. https://doi.org/10.1088/1742-5468%2F2010%2F04%2Fp04021

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