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By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g., associativity, commutativity and existence of neutral… (More)

We investigate three different approaches for fitting the degree distributions of China-, USand the composite China+US air network, in order to reveal the nature of such distributions and the potential theoretical background on which they are based. Our first approach is the fitting with q-statistics probability distribution, done separately in two regimes.… (More)

- Y. Kaupp, S. Liraki, +7 authors Q. A. Wang
- 2008

Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model. Numerical results have shown that the Fermi surface of these correlated particles undergoes a flattening effect according to the coupling degree J. This behaviour is not easy to understand from the theoretical point of view within standard Fermi-Dirac… (More)

- A. Le Méhauté, A. El Kaabouchi, L. Nivanen
- Computers & Mathematics with Applications
- 2010

This is a study of the information evolution of complex systems by a geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness of the state number counting at any scale on… (More)

In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or Rényi statistics for nonextensive systems at equilibrium; 2) equilibrium N -body systems with nonadditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic equilibrium. The… (More)

In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or Rényi statistics for nonextensive systems at meta-equilibrium; 2) N -body systems with nonadditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic stationarity. 3) the… (More)

We discuss a possibility of establishing a nonextensive incomplete statistics based on Tsallis entropy for equilibrium systems with different q values. PACS : 02.50.-r, 05.20.-y, 05.70.-a

This is a study of composition rule and temperature definition for nonextensive systems containing different q subsystems. The physical meaning of the multiplier β associated with the energy expectation in the optimization of Tsallis entropy is investigated for the formalism with normalized expectation given by escort probability. This study is carried out… (More)

In this work, we consider a recently proposed entropy I (called varentropy) defined by a variational relationship ) ( dx x d dI − = β as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized virtual work principle 0 = dx leading to maximum entropy 0 ) ( = − x I d β . This paper presents an analytical investigation… (More)