Dynamics and statistics of the Fermi–Pasta–Ulam<i>β</i>-model with different ranges of particle interactions

Christodoulidi, Helen; Bountis, Tassos; Tsallis, Constantino; Drossos, L.

doi:10.1088/1742-5468/aa4f0e

Cited by 43 publications

(52 citation statements)

References 38 publications

(57 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The third and last regime, from α A /d ≃ 5 on, is Boltzmannian-like and is characterized by short-range interactions. The existence of the intermediate regime has also been observed in classical many-body Hamiltonians, namely the α-generalized XY [16,17] and Heisenberg [18] rotator models as well as the Fermi-Pasta-Ulam model [19,20,[29][30][31]. The present work neatly illustrates a fact which is not always obvious to the community working with complex networks, more precisely those exhibiting asymptotic scale-free behavior.…”

Section: Resultssupporting

confidence: 66%

Scaling properties of d -dimensional complex networks

et al. 2019

Self Cite

View full text Add to dashboard Cite

The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located d-dimensional networks. In this paper, we study scaling properties of a wide class of d-dimensional geographically located networks which grow with preferential attachment involving Euclidean distances through r −α A ij (αA ≥ 0). We have numerically analyzed the time evolution of the connectivity of sites, the average shortest path, the degree distribution entropy, and the average clustering coefficient, for d = 1, 2, 3, 4, and typical values of αA. Remarkably enough, virtually all the curves can be made to collapse as functions of the scaled variable αA/d. These observations confirm the existence of three regimes. The first one occurs in the interval αA/d ∈ [0, 1]; it is non-Boltzmannian with verylong-range interactions in the sense that the degree distribution is a q-exponential with q constant and above unity. The critical value αA/d = 1 that emerges in many of these properties is replaced by αA/d = 1/2 for the β-exponent which characterizes the time evolution of the connectivity of sites. The second regime is still non-Boltzmannian, now with moderately long-range interactions, and reflects in an index q monotonically decreasing with αA/d increasing from its critical value to a characteristic value αA/d ≃ 5. Finally, the third regime is Boltzmannian-like (with q ≃ 1), and corresponds to short-range interactions. *

show abstract

Section: Resultssupporting

confidence: 66%

Scaling properties of d -dimensional complex networks

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Theoretical and experimental illustrations in natural systems include long-range-interacting many-body classical Hamiltonian systems [13][14][15][16][17][18][19][20] (see also [21,22] [47,48], chemistry [49], earthquakes [50], biology [51,52], solar wind [53,54], anomalous diffusion in relation to central limit theorems and overdamped systems [55][56][57][58][59][60][61][62][63][64], quantum entangled systems [65,66], quantum chaos [67], astronomical systems [68,69], thermal conductance [70], mathematical structures [71][72][73][74][75][76] and nonlinear quantum mechanics [77][78][79][80][81][82][83][84]…”

Section: Introductionmentioning

confidence: 99%

Economics and Finance: q-Statistical Stylized Features Galore

Tsallis

2017

Entropy

Self Cite

View full text Add to dashboard Cite

Abstract:The Boltzmann-Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy S q (q ∈ R), which recovers the BG entropy in the q → 1 limit. The optimization of S q under appropriate simple constraints straightforwardly yields the so-called q-exponential and q-Gaussian distributions, respectively generalizing the exponential and Gaussian ones, recovered for q = 1. These generalized functions ubiquitously emerge in complex systems, especially as economic and financial stylized features. These include price returns and volumes distributions, inter-occurrence times, characterization of wealth distributions and associated inequalities, among others. Here, we briefly review the basic concepts of this q-statistical generalization and focus on its rapidly growing applications in economics and finance.

show abstract

“…and the q-Gaussian exp q [−βx 2 ] appear naturally by extremizing S q under appropriate constraints [27][28][29]. The generalized thermostatistics based on S q frequently applies when assumptions underlying the BG thermostatistics are not fulfilled (like, e.g., mixing and ergodicity) [14,15,[18][19][20][29][30][31][32][33][34].…”

mentioning

confidence: 99%

Validity and failure of the Boltzmann weight

Cirto¹,

Rodríguez²,

Nobre³

et al. 2018

EPL

View full text Add to dashboard Cite

The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on d-dimensional lattices (d = 1, 2, and 3), through molecular dynamics. The interactions between rotators decay with the distance r ij like 1/r α ij (α ≥ 0), where α → ∞ and α = 0 respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas q-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to q-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on d and α through the ratio α/d. * Electronic address: cirto@cbpf.br † Electronic address: antonio.rodriguezm@upm.es ‡ Electronic address: fdnobre@cbpf.br § Electronic address: tsallis@cbpf.br

show abstract

Dynamics and statistics of the Fermi–Pasta–Ulamβ-model with different ranges of particle interactions

Cited by 43 publications

References 38 publications

Scaling properties of d -dimensional complex networks

Scaling properties of d -dimensional complex networks

Economics and Finance: q-Statistical Stylized Features Galore

Validity and failure of the Boltzmann weight

Contact Info

Product

Resources

About