arXiv subjects
Publications and source records attributed to Andrei G. Bashkirov.
It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.
Effective potential of a charged dusty particle moving in homogeneous plasma has a negative part that provides attraction between similarly charged dusty particles. A depth of this potential well is great enough to ensure both stability of crystal structure of dusty plasma and sizable value of surface tension of a boundary surface of dusty region. The latter depends on the orientation of the surface relative to the counter-ion flow, namely, it is maximal and positive for the surface normal to the flow and minimal and negative for the surface along the flow. For the most cases of dusty plasma in a gas discharge, a value of the first of them is more than sufficient to ensure stability of lenticular dusty phase void oriented across the counter-ion flow.
The Renyi entropy with a free Renyi parameter $q$ is the most justified form of information entropy, and the Tsallis entropy may be regarded as a linear approximation to the Renyi entropy when $q\simeq 1$. When $q\to 1$, both entropies go to the Boltzmann--Shannon entropy. The application of the principle of maximum of information entropy (MEP) to the Renyi entropy gives rise to the microcanonical (homogeneous) distribution for an isolated system. Whatever the value of the Renyi parameter $q$ is, in this case the Renyi entropy becomes the Boltzmann entropy $S_B=k_B\ln W$, that provides support for universality of the Boltzmann's principle of statistical mechanics. For a system being in contact with a heat bath, the application of MEP to the Renyi entropy gives rise to Levy distribution (or, $q$-distribution) accepted as one of the main results of the so-called nonextensive statistics. The same distribution is derived here for a small physical system experiencing temperature fluctuations. The long--range "tail" of the Levy distribution is the power--law (Zipf-Pareto) distribution with the exponent $s$ expressed via $q$. The exponent and free Renyi parameter $q$ can be uniquely determined with the use of a further extension of MEP. Then typical values of $s$ are found within the range $1.3÷2$ and of $q$ within the range $0.25÷0.5$, in dependence on parameters of stochastic systems.