Comments on "Stability of Tsallis entropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions"

It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.Comment: 1 pag

Long-range attraction between particles in dusty plasma and partial surface tension of dusty phase boundary

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.Comment: LATEX, REVTEX4, 7 pages, 6 figure

Maximum Renyi entropy principle for systems with power--law Hamiltonian

The Renyi distribution ensuring the maximum of a Renyi entropy is investigated for a particular case of a power--law Hamiltonian. Both Lagrange parameters, $\alpha$ and $\beta$ can be excluded. It is found that $\beta$ does not depend on a Renyi parameter $q$ and can be expressed in terms of an exponent $\kappa$ of the power--law Hamiltonian and an average energy $U$. The Renyi entropy for the resulted Renyi distribution reaches its maximal value at $q=1/(1+\kappa)$ that can be considered as the most probable value of $q$ when we have no additional information on behaviour of the stochastic process. The Renyi distribution for such $q$ becomes a power--law distribution with the exponent $-(\kappa +1)$. When $q=1/(1+\kappa)+\epsilon$ ($0<\epsilon\ll 1$) there appears a horizontal "head" part of the Renyi distribution that precedes the power--law part. Such a picture corresponds to observables.Comment: LaTeX, 7 pages, 4 figure

Noether's second theorem in a general setting. Reducible gauge theories

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means of certain intertwining operator is proved.Comment: 20 pages, to be published in J. Phys. A (2005