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Density operators that extremize Tsallis entropy and thermal stability effects

C. Vignat·A. Plastino
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Abstract

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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C. Vignat, A. Plastino. 2005-05-06. Density operators that extremize Tsallis entropy and thermal stability effects. https://doi.org/10.1016/j.physa.2005.07.013

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