2019/11/01 by Jean-Pierre Gazeau, Constantino Tsallis · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.3390/e21121155
Keyword: non-additive entropy; q-statistics; Möbius transform; complex systems
arxiv created 2019/11/01 · arxiv updated 2020/01/08
In the realm of Boltzmann-Gibbs (BG) statistical mechanics and its q-generalisation for complex systems, we analyse observed sequences of q-triplets, or q-doublets if one of them is the unity, in terms of cycles of successive Möbius transforms of the line preserving unity ( q=1 corresponds to the BG theory). Such transforms have the form q --> (aq + 1-a)/[(1+a)q -a], where a is a real number; the particular cases a=-1 and a=0 yield respectively q --> (2-q) and q --> 1/q, currently known as additive and multiplicative dualities. This approach seemingly enables the organisation of various complex phenomena into different classes, named N-complete or incomplete. The classification that we propose here hopefully constitutes a useful guideline in the search, for non-BG systems whenever well described through q-indices, of new possibly observable physical properties.