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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 eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.

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)

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)

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). PACS: 05.20.-y, 05.20.Jj,… (More)

- Aristóteles Góes-Neto, Marcelo V. C. Diniz, +6 authors Roberto F. S. Andrade
- 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)

- Ernesto P. Borges, Constantino Tsallis, Garín F J Añaños, Paulo Murilo Castro de Oliveira
- Physical review letters
- 2002

We consider nonequilibrium probabilistic dynamics in logisticlike maps x(t+1)=1-a|x(t)|(z), (z>1) at their chaos threshold: We first introduce many initial conditions within one among W>>1 intervals partitioning the phase space and focus on the unique value q(sen)<1 for which the entropic form S(q) identical with (1- summation operator Wp(q)(i))/(q-1)… (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 qmix ≤ 1) and equilibration (characterized by the entropic index qeq ≥ 1) play central and inter-related roles, and appear to determine a priori the values of the relevant indices of the… (More)

We propose a two-parametric non-distributive algebraic structure that follows from (q, q)-logarithm and (q, q)-exponential functions. Properties of generalized (q, q)operators are analyzed. We also generalize the proposal into a multi-parametric structure (generalization of logarithm and exponential functions and the corresponding algebraic operators). All… (More)

We discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian Mean Field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann-Gibbs exponential weight in Gibbs Γ-space of microscopic configurations, and comment a paper recently published by Baldovin and… (More)