Tsallis distribution with complex nonextensivity parameter q
  We discuss a Tsallis distribution with complex nonextensivity parameter $q$. In this case the usual distribution is decorated with a log-periodic oscillating factor (apparently, such oscillations can bee seen in recently measured transverse momentum distributions in collisions at very high energies). Complex $q$ also means complex heat capacity which shall also be briefly discussed. 
G. Wilk and Z.Wlodarczyk
cond-mat.stat-mech hep-ph