Tsallis' entropy maximization procedure revisited

The proper way of averaging is an important question with regards to Tsallis' Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP) normalization procedure, exhibits clear advantages with respect to earlier ones. In this work, we advance a distinct (from the TMP-one) way of handling the Lagrange multipliers involved in the extremization process that leads to Tsallis' statistical operator. It is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the Tsallis-Mendes-Plastino formalism.