Non-distributive algebraic structures derived from nonextensive   statistical mechanics
  We propose a two-parametric non-distributive algebraic structure that follows from $(q,q')$-logarithm and $(q,q')$-exponential functions. Properties of generalized $(q,q')$-operators are analyzed. We also generalize the proposal into a multi-parametric structure (generalization of logarithm and exponential functions and the corresponding algebraic operators). All $n$-parameter expressions recover $(n-1)$-generalization when the corresponding $q_n\to1$. Nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures, in which this work is a consequence. 
Pedro G. S. Cardoso, Ernesto P. Borges, Thierry C. P. Lob\~ao, Suani   T. R. Pinho