Nilpotence in Physics: the case of Tsallis entropy
  In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of $3\times 3$ upper triangular matrices with real entries. We explore consequences of this embedding and of the geometry of the ambient $3\times 3$ Heisenberg group. This approach establishes the polynomial growth of the volume of phase space of systems described by the Tsallis entropy and provides a general framework for understanding Abe's formula in terms of the Pansu derivative between Riemannian spaces. 
Anthony J. Creaco, Nikos Kalogeropoulos
math-ph cond-mat.stat-mech math.MP