Thermodynamics’ zeroth law in a nonextensive scenario

We show how to reconcile Tsallis’ thermostatistics with thermodynamics’ zeroth law, by recourse to the so-called optimal Lagrange multipliers formalism. The central concept is that of not identifying in the usual fashion the inverse temperature with the Lagrange multiplier associated to the internal energy. Our analysis provides one with compatibility conditions between the additivity of the internal energy and the pseudo-additivity of the generalized entropy. With regards to the first law of thermodynamics, a generalization of Clausius’ equation is advanced.