Incomplete statistics: nonextensive generalizations of statistical mechanics

Statistical mechanics is generalized on the basis of incomplete information theory for inexact or incomplete probability distribution. An incomplete normalization Sigma (w)(i=1), p(i)(q) = 1 with positive real q is proposed and, thanks to the q-deformed logarithmic function used as information measure I-q(N) = N1-q-1/1-q, leads to a nonextensive entropy: [GRAPHICS] The resulting incomplete statistical mechanics is proved to have the same theoretical characteristics as the Tsallis one for complete probability distributions. (C) 2001 Elsevier Science Ltd. All rights reserved.