A fractal approach to the distribution function of a paramagnetic system

Thermodynamics of boson and fermion systems with fractal distribution functions

“…We should remark that for the boson case our partition function differs from the factorized partition function considered in Ref. [9]. A calculation of the heat capacity that results from the boson generalized distribution function shows that it is continuous at the critical temperature.…”

“…(2) and nonextensive thermodynamics are not unrelated. In fact, these fractal distributions have also been obtained [9] by considering the case of a dilute gas and approximating the partition function in Eq. (7) with a factorized partition function.…”

Bec in Nonextensive Statistical Mechanics

“…2 The NSM is characterized by a parameter q such that (q − 1) is a measure of the lack of extensivity: in the limit q → 1 one recovers the familiar statistical mechanics but for q = 1 one obtains generalized Boltzmann, Fermi and Bose distributions. 3 In the last few years the NSM has been applied in different contexts like solar neutrinos, 4 high energy nuclear collisions 5 and the cosmic microwave background radiation. 6 In such cases it has been found that a small deviation from standard statistics is sufficient for eliminating the discrepancy between theoretical calculations and experimental data.…”

Change in the quantum information difference during evoluton of nonextensive systems in the space of control parameters

“…imposed on the distributions are not satisfied, self-organization is not observed in the examined processes, and other criteria of system microstate ordering are required. For 1 q = , we have results obtained in [9] for quantum systems with entropy (6) and information difference (7). The extreme properties of the information difference and theorems for the Fermi gases are proved analogously.…”

“…Entropy (3) and information difference (4) were introduced for the first time in [7,8]. Moreover, the approach based on multifractal theory was used in [7], and in [8] conclusion was based on the Bregman functional used in the theory of linear and convex programming and generalized to the nonextensive systems. …”