Compatibility between dynamics and Tsallis statistics

Carati, A.

doi:10.1063/1.2828758

AIP Conference Proceedings

2007

DOI: 10.1063/1.2828758

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Compatibility between dynamics and Tsallis statistics

A. Carati¹

Abstract: We perform numerical simulations for the dynamics of a chain of weakly coupled particles, and consider the process of occupation of cells in phase space, in the spirit of paper [1]. A different behaviour is exhibited as the coupling constant is changed. It is discussed whether such a dynamical behaviour is compatible with the Tsallis statistics.

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2014

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Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics

Christodoulidi¹,

Tsallis²,

Bountis³

2014

EPL

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We introduce and numerically study a long-range-interaction generalization of the one-dimensional Fermi-Pasta-Ulam (FPU) β− model. The standard quartic interaction is generalized through a coupling constant that decays as 1/r α (α ≥ 0)(with strength characterized by b > 0). In the α → ∞ limit we recover the original FPU model. Through classical molecular dynamics computations we show that (i) For α ≥ 1 the maximal Lyapunov exponent remains finite and positive for increasing number of oscillators N (thus yielding ergodicity), whereas, for 0 ≤ α < 1, it asymptotically decreases as N −κ(α) (consistent with violation of ergodicity); (ii) The distribution of time-averaged velocities is Maxwellian for α large enough, whereas it is well approached by a q-Gaussian, with the index q(α) monotonically decreasing from about 1.5 to 1 (Gaussian) when α increases from zero to close to one. For α small enough, the whole picture is consistent with a crossover at time t c from q-statistics to Boltzmann-Gibbs (BG) thermostatistics. More precisely, we construct a "phase diagram" for the system in which this crossover occurs through a frontier of the form 1/N ∝ b δ /t γ c with γ > 0 and δ > 0, in such a way that the q = 1 (q > 1) behavior dominates in the lim N →∞ lim t→∞ ordering (lim t→∞ lim N →∞ ordering).

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Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics

Christodoulidi¹,

Tsallis²,

Bountis³

2014

EPL

View full text Add to dashboard Cite

show abstract

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Compatibility between dynamics and Tsallis statistics

Cited by 1 publication

References 14 publications

Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics

Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics

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