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We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigen-function. The q-derivative and the q-integral have a dual nature, that is also presented .

The analysis of cosmic rays fluxes as a function of energy reveals a knee slightly below 10 16 eV and an ankle close to 10 19 eV. Their physical origins remain up to now quite enigmatic; in particular, no elementary process is known which occurs at energies close to 10 16 eV. We propose a phenomeno-logical approach along the lines of nonextensive… (More)

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… (More)

We analyze the cumulative distribution of total personal income of USA counties, and gross domestic product of Brazilian, German and United Kingdom counties, and also of world countries. We verify that generalized exponential distributions, related to nonextensive statistical mechanics, describe almost the whole spectrum of the distributions (within… (More)

We study, through molecular dynamics, a conservative two-dimensional Lennard-Jones-like gas (with attractive potential ∝ r −α). We consider the effect of the range index α of interactions, number of particles, total energy and particle density. We detect negative specific heat when the interactions become long-ranged (0 ≤ α/d < 1). Non-Gaussian equilibrium… (More)

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent the transitions between these regions. Parameters used to quantify the properties of complex networks, including those… (More)

- Ugur Tirnakli, Ernesto P. Borges
- Scientific reports
- 2016

As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that… (More)

Context. We investigate the distribution of asteroid rotation periods from different regions of the solar system and diameter distributions of near-Earth asteroids (NEAs). Aims. We aim to verify if nonextensive statistics satisfactorily describes the data. Methods. Light curve data were taken from the Planetary Database System (PDS) with Rel ≥ 2. We also… (More)

- Aristoteles Goes-Neto, Marcelo V. C. Diniz, Leonardo B. L. Santos, Suani T. R. Pinho, José G. V. Miranda, Thierry Petit Lobão +3 others
- Biosystems
- 2010

Chitin is a structural endogenous carbohydrate, which is a major component of fungal cell walls and arthropod exoskeletons. A renewable resource and the second most abundant polysaccharide in nature after cellulose, chitin is currently used for waste water clearing, cosmetics, medical, and veterinary applications. This work comprises data mining of protein… (More)

After a brief review of the present status of nonextensive statistical mechanics , we present a conjectural scenario where mixing (characterized by the entropic index q mix ≤ 1) and equilibration (characterized by the entropic index q eq ≥ 1) play central and interrelated roles, and appear to determine a priori the values of the relevant indices of the… (More)