We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter q > 1 we advance an alternative cut-off prescription and discuss some of its basic mathematical properties.As an illustration of the new cut-off prescription we consider in some detail the q-generalized quantum distributions which have recently been shown to reproduce various experimental results related to high T c superconductors.

The q-deformed statistics for fermions arising within the non-extensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aim of the present note is to point out some subtle difficulties presented by this approach in connection with the problem of thermodynamic consistency. Different possible ways to apply the q-deformed quantum distributions in a thermodynamically consistent way are considered.

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The aim of this paper is to investigate the effect of a non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quarkgluon plasma (QGP). We suggest to account for the effects of the dominant part of the long-range interactions among the constituents in the QGP by a change in the statistics of the system in this phase, and we study the relevance of this statistics for the phase transition. The results show that small deviations (≈ 10%) from Boltzmann-Gibbs statistics in the QGP produce a noticeable change in the phase diagram, which can, in principle, be tested experimentally.1

The effect of the non-extensive form of statistical mechanics pro-

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The generalized non-extensive statistics proposed by Tsallis have been successfully utilized in many systems where long range interactions are present. For high density quark matter an attractive long range interaction arising from single gluon exchange suggests the formation of a diquark condensate. We study the effects on this color superconducting phase for two quark flavors due to a change to Tsallis statistics. By numerically solving the gap equation we obtain a generalization of the universality condition, 2φ 0 T C ≈ 3.52 and determine the temperature dependence of the gap. For the Tsallis parameter q ≈ 1 the specific heat is exponential becoming more linear as q increases. This suggests that for larger values of q s-wave color superconductors behave like high T c superconductors rather than weak superconductors.