Evolution of the difference information in the process of the Fermi and Bose gas self-organization for nonextensive systems

Abstract

A theoretical-informational description of transitions between stationary states in the control parameter space is given for quantum nonextensive self-organized systems. A new measure of the difference information is given, and the S-and I-theorems on changes of parameterized quantum entropy and difference information measures are proved under the Gibbs condition for the Hamilton effective function.

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

“…According to the theoretical-informational approach [8][9][10][11]13], we now require that the additivity law 0 q q I I I = + be true for all values of the control parameters, that is, equate quantities given by Eqs. (15) and (16).…”

“…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.…”

“…The results obtained in [12,13] were generalized to quantum systems with functionals (6) and (7) in [9]. Based on the results obtained in [9][10][11][12][13], the evolution of entropy (3) and information difference (4) for a preset effective Hamilton function was further studied in [8]. In general, the effective Hamilton functions are unknown, which calls for additional consideration.…”

“…Inequalities (22) are local forms of the S-and I-theorems. We note that under additional conditions(10), the distribution 0 f maximizes the is a quantum analog of the auxiliary distribution used for the definition of the comparative degree of open system state ordering[8][9][10][11][12][13]. The extreme properties of the information difference and entropy allowed us to establish principal limits of changing q I during self-…”