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With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namely Sq==-k[1-Zwt pq]/(q-1), where qe~ characterizes the generalization and {Pi} are the probabilities associated with W (microscopic) configurations (WE N). The main properties associated with this entropy are established, particularly those… (More)

- Constantino Tsallis, Xavier Sigaud, Josiah Willard
- 2009

- M Gell-Mann, C Tsallis, Armin Bunde, Jan Eichner, Rathinaswamy Govindan, Shlomo Havlin +3 others
- 2002

We review recent results on the appearance of long-term persistence in climatic records and their relevance for the evaluation of global climate models and rare events. The persistence can be characterized, for example, by the correlation C(s) of temperature variations separated by s days. We show that, contrary to previous expectations, C(s) decays for… (More)

The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns nonextensive systems, where nonextensivity is understood in the thermody-namical sense. This generalization was first proposed in 1988… (More)

- Constantino Tsallis, Marcio P De Albuquerque
- 2008

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 4, 131 (1998)]. To fit the data, a stretched exponential (N(x) ∝ exp −(x/x 0) β) has been used with only partial success. The success is not complete because the data exhibit, for large citation count x, a… (More)

- V Schwammle, E M F Curado, F D Nobre, S Abe, H Herrmann, P Quarati +2 others
- 2007

Proving the H-theorem by making use of nonlinear Fokker-Planck equations leads to classes of these equations related to the same entropy and their equilibrium state corresponds to the one obtained by maximizing such an entropy under constraints of an external potential. In the present work, the numerical integration of a subset of the class associated to… (More)

We propose a new stochastic algorithm (generalized simulated an-nealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm recovers, as particular cases, the so called classical (" Boltzmann machine ") and fast (" Cauchy machine ") simulated… (More)

The q-Gaussian distribution is known to be an attractor of certain correlated systems, and is the distribution which, under appropriate constraints, maximizes the entropy S q , the basis of nonextensive statistical mechanics. This theory is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and may explain the… (More)

Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently introduced by one of us (C.T.) and characterized by the entropic index q. We show that general scaling arguments imply that… (More)

- Constantino Tsallis, Dirk Jan Bukman
- 1996

The optimization of the usual entropy S 1 [p] = − du p(u) ln p(u) under appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing an important class of normal diffusions. We show here that the optimization of the generalized entropic form S q [p] = {1 − du [p(u)] q }/(q − 1)… (More)