About an alternative distribution function for fractional exclusion statistics

We show that it is possible to replace the actual implicit distribution function of the fractional exclusion statistics by an explicit one whose form does not change with the parameter $\alpha$. This alternative simpler distribution function given by a generalization of Pauli exclusion principle from the level of the maximal occupation number is not completely equivalent to the distributions obtained from the level of state number counting of the fractional exclusion particles. Our result shows that the two distributions are equivalent for weakly bosonized fermions ($\alpha>>0$) at not very high temperatures.Comment: 8 pages, 3 eps figures, TeX. Nuovo Cimento B (2004), in pres

How to proceed with nonextensive systems at equilibrium?

In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or R\'enyi 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 equivalence of Tsallis and R\'enyi entropies is in general not true.Comment: 14 pages, TEX, no figur

About "On certain incomplete statistics" by Lima et al

Lima et al recently claim that ({\em Chaos, Solitons & Fractals,} 2004;19:1005)the entropy for the incomplete statistics based on the normalization$\sum_ip_i^q=1$ should be $S=-\sum_ip_i^{2q-1}\ln_qp_i$ instead of$S=-\sum_ip_i^{q}\ln_qp_i$ initially proposed by Wang. We indicate here that thisconclusion is a result of erroneous use of temperature definition for the incompletestatistics

Fractal geometry, information growth and nonextensive thermodynamics

This is a study of the information evolution of complex systems by 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 fractal support, the incomplete normalization $\sum_ip_i^q=1$ is applied throughout the paper, where $q$ is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the trace-form $\sum_ip_i-\sum_ip_i^q$ which can be connected to several nonadditive entropies. This information growth can be extremized to give power law distributions for these non-equilibrium systems. It can also be used for the study of the thermodynamics derived from Tsallis entropy for nonadditive systems which contain subsystems each having its own $q$. It is argued that, within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can be preserved.Comment: Final version, 10 pages, no figures, Invited talk at the international conference NEXT2003, 21-28 september 2003, Villasimius (Cagliari), Ital