Density operators that extremize Tsallis entropy and thermal stability effects

Details Density operators that extremize Tsallis entropy and thermal stability effects Density operators that extremize Tsallis entropy and thermal stability effects

2005-05-06

arxiv.org/abs/cond-mat/0505158v1

Physics

Condensed Matter

Statistical Mechanics

22 pages

Scientific paper

10.1016/j.physa.2005.07.013

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PD's as "weights" leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis' non-extensivity index $q$ one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy.

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