Are citations of scientific papers a case of nonextensivity ?

The distribution $N(x)$ of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner [Eur. Phys. J. B {\bf 4}, 131 (1998)]. To fit the data, a stretched exponential ($N(x) \propto \exp{-(x/x_0)^{\beta}}$) has been used with only partial success. The success is not complete because the data exhibit, for large citation count $x$, a power law (roughly $N(x) \propto x^{-3}$ for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism, the same data can be quite satisfactorily fitted with a single curve (namely, $N(x) \propto 1/[1+(q-1) \lambda x]^{q/{q-1}}$ for the available values of $x$. This is consistent with the connection recently established by Denisov [Phys. Lett. A {\bf 235}, 447 (1997)] between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number $x$.Comment: Revtex,1 Figure postscript;[email protected]

Weak Chaos in large conservative system -- Infinite-range coupled standard maps

We study, through a new perspective, a globally coupled map system that essentially interpolates between simple discrete-time nonlinear dynamics and certain long-range many-body Hamiltonian models. In particular, we exhibit relevant similarities, namely (i) the existence of long-standing quasistationary states (QSS), and (ii) the emergence of weak chaos in the thermodynamic limit, between the present model and the Hamiltonian Mean Field model, a strong candidate for a nonxtensive statistical mechanical approach.Comment: 6 pages, 2 figures. Corrected typos in equation 4. Changed caption in Fig. 1. Corrected references 2 and 6. Acknowledgements adde

Nonextensive statistical mechanics - Applications to nuclear and high energy physics

A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system appears to relax, along time, on macroscopic states which violate the ergodic assumption. Some of these phenomena appear to follow, instead, the prescriptions of nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy $S_{BG}=-k \sum_i p_i \ln p_i$, the nonextensive one is based on the form $S_q=k(1-\sum_ip_i^q)/(q-1)$ (with $S_1=S_{BG}$). Typically, the systems following the rules derived from the former exhibit an {\it exponential} relaxation with time toward a stationary state characterized by an {\it exponential} dependence on the energy ({\it thermal equilibrium}), whereas those following the rules derived from the latter are characterized by (asymptotic) {\it power-laws} (both the typical time dependences, and the energy distribution at the stationary state). A brief review of this theory is given here, as well as of some of its applications, such as electron-positron annihilation producing hadronic jets, collisions involving heavy nuclei, the solar neutrino problem, anomalous diffusion of a quark in a quark-gluon plasma, and flux of cosmic rays on Earth. In addition to these points, very recent developments generalizing nonextensive statistical mechanics itself are mentioned.Comment: 23 pages including 5 figures. To appear in the Proceedings of the Xth International Workshop on Multiparticle Production - Correlations and Fluctuations in QCD (8-15 June 2002, Crete), ed. N. Antoniou (World Scientific, Singapore, 2003). It includes a reply to the criticism expressed in R. Luzzi, A.R. Vasconcellos and J.G. Ramos, Science 298, 1171 (2002

Jakriborg, Suecia: reflexión en torno a un particular caso de diseño urbano en el contexto de los movimientos neotradicionales. / Jakriborg, Sweden: a case of urban design in the scenario of neo-traditional movements.

Como parte de un enfoque crítico al crecimiento incremental disperso y difuso en las periferias urbanas y territorios rurales adyacentes a la ciudad contemporánea, surgen diversas corrientes urbanísticas entre las cuales se encuentran las que buscan instalar modelos alternativos que ofrezcan mejores condiciones de habitabilidad y sostenibilidad desde una aproximación caracterizada en las últimas décadas como diseño urbano neotradicional. A diferencia del urbanismo culturalista, estas corrientes se sustentan en un cuerpo de principios esencialmente pragmático que recoge lo mejor del pasado, reconociendo el presente, para proyectarlo hacia los desafíos que supone el futuro del desarrollo urbano. El caso sueco de Jakriborg tratado en este artículo, es una experiencia singular que permite entender de mejor manera el debate que se genera en torno a la pertinencia de las corrientes neotradicionales en el contexto de los desafíos actuales, ya que constituye un caso que pareciera extremar el imaginario historicista por sobre otras consideraciones, si bien aporta otros fundamentos que enriquecen su propuesta de diseño. / As a part of a critical approach to sprawl in contemporary urban growth, diverse urban planning and design movements emerge, some of which seek to provide better living conditions and sustainability by engaging in neo-traditional planning and design. Unlike the urban culturalists, these currents are based on an essentially pragmatic body of principles that gathers together the best of the past, acknowledges the present, to project them towards the challenges of future urban development. The case of Jakriborg, Sweden, discussed in this article, is a particular experience that allows a better understanding of the debate on the pertinence of neo-traditional movements in the actual context and in its challenges. It constitutes an experience that seems to favor a historicist imagery over further considerations, while nevertheless, bringing up other aspects that enrich their design proposal

General properties of nonlinear mean field Fokker-Planck equations

Recently, several authors have tried to extend the usual concepts of thermodynamics and kinetic theory in order to deal with distributions that can be non-Boltzmannian. For dissipative systems described by the canonical ensemble, this leads to the notion of nonlinear Fokker-Planck equation (T.D. Frank, Non Linear Fokker-Planck Equations, Springer, Berlin, 2005). In this paper, we review general properties of nonlinear mean field Fokker-Planck equations, consider the passage from the generalized Kramers to the generalized Smoluchowski equation in the strong friction limit, and provide explicit examples for Boltzmann, Tsallis and Fermi-Dirac entropies.Comment: Paper presented at the international conference CTNEXT07, 1-5 july 2007, Catania, Ital

Time evolution of nonadditive entropies: The logistic map

Due to the second principle of thermodynamics, the time dependence of entropy for all kinds of systems under all kinds of physical circumstances always thrives interest. The logistic map $x_{t+1}=1-a x_t^2 \in [-1,1]\;(a\in [0,2])$ is neither large, since it has only one degree of freedom, nor closed, since it is dissipative. It exhibits, nevertheless, a peculiar time evolution of its natural entropy, which is the additive Boltzmann-Gibbs-Shannon one, $S_{BG}=-\sum_{i=1}^W p_i \ln p_i$, for all values of $a$ for which the Lyapunov exponent is positive, and the nonadditive one $S_q= \frac{1-\sum_{i=1}^W p_i^q}{q-1}$ with $q=0.2445\dots$ at the edge of chaos, where the Lyapunov exponent vanishes, $W$ being the number of windows of the phase space partition. We numerically show that, for increasing time, the phase-space-averaged entropy overshoots above its stationary-state value in all cases. However, when $W\to\infty$, the overshooting gradually disappears for the most chaotic case ($a=2$), whereas, in remarkable contrast, it appears to monotonically diverge at the Feigenbaum point ($a=1.4011\dots$). Consequently, the stationary-state entropy value is achieved from {\it above}, instead of from {\it below}, as it could have been a priori expected. These results raise the question whether the usual requirements -- large, closed, and for generic initial conditions -- for the second principle validity might be necessary but not sufficient.Comment: 7 pages, 6 composed figures (total of 15 simple figures

Nonlinear dynamical systems: Time reversibility {\it versus} sensitivity to the initial conditions

Time reversal of vast classes of phenomena has direct implications with predictability, causality and the second principle of thermodynamics. We analyze in detail time reversibility of a paradigmatic dissipative nonlinear dynamical system, namely the logistic map $x_{t+1}=1-ax_t^2$. A close relation is revealed between time reversibility and the sensitivity to the initial conditions. Indeed, depending on the initial condition and the size of the time series, time reversal can enable the recovery, within a small error bar, of past information when the Lyapunov exponent is non-positive, notably at the Feigenbaum point (edge of chaos), where weak chaos is known to exist. Past information is gradually lost for increasingly large Lyapunov exponent (strong chaos), notably at $a=2$ where it attains a large value. These facts open the door to diverse novel applications in physicochemical, astronomical, medical, financial, and other time series.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:2211.0326