Nonextensive normalized treatment of Clausius equation

We revisit the first law of thermodynamics for nonextensive statistics by recourse to the optimal Lagrange multipliers (OLM) formalism. We show firstly that information theory allows one to obtain thermodynamics' first law in a general ensemble by dealing just with variations in the density operator, without disturbing the system's Hamiltonian. After re-deriving Clausius equation we discuss it in some detail and show that for the Tsallis-Mendes-Plastino (TMP) normalization: (i) Nonextensive reversible processes connecting off-equilibrium states exist, (ii) for any extensive reversible process between equilibrium states one can find some other, equivalent nonextensive irreversible one, and (iii) in some circumstances, an extensive irreversible process can be assimilated to a nonextensive reversible one.