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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)

The definitions of the temperature in the nonextensive statistical thermodynamics based on Tsallis entropy are analyzed. A definition of pressure is proposed for nonadditive systems by using a nonadditive effective volume. The thermodynamics of nonadditive photon gas is discussed on this basis. We show that the Stefan-Boltzmann law can be preserved within… (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 nonad-ditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic equilibrium. The… (More)

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)

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 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)

This is a study of the information evolution of complex systems through 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 information calculation in fractal… (More)

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

Equilibrium or meta-equilibrium incomplete thermostatistics with different q indices Abstract We discuss a possibility of establishing a nonextensive incomplete statistics based on Tsallis entropy for equilibrium systems with different q values.

We investigate three different approaches for fitting the degree distributions of China-, US-and 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… (More)