A short review of elementary properties and possible applications of deformed q-algebra derived from non-extensive Tsallis entropy

摘要

Tsallis entropy introduced in 1988 is considered to have obtained new possibilities to construct generalized thermodynamical basement for statistical physics expanding classical Boltzmann-Gibbs-Shannon thermodynamics for non-equilibrium states. During the last two decades this q-generalized theory has been successfully applied to a considerable amount of physically interesting complex phenomena. The authors would like to present a short rewiev, the applications and the elementary properties of some operators in deformed q-algebra derived from Tsallis definition of non-extensive entropy based on the definitions of the q-logarithm and the q-exponential. The new definition of the q-root is also introduced.