Density matrix for a consistent non-extensive thermodynamics

Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density matrix operators and hamiltonians. In particular, for the bosonic case the corresponding operators satisfy a deformed bosonic algebra and the hamiltonian involves interacting terms in powers of \(a^{\dagger}_ja_j\) standard creation and annihilation operators. For the unnormalized density matrix we obtain a nonlinear equation that leads to a two-parameter solution relevant to anomalous diffusion phenomena.