Incremental Entropy Relation as an Alternative to MaxEnt

We show that, to generate the statistical operator appropriate for a given system, and as an alternative to Jaynes’ MaxEnt approach, that refers to the entropy S, one can use instead the increments δS in S. To such an effect, one uses the macroscopic thermodynamic relation that links δS to changes in i) the internal energy E and ii) the remaining M relevant extensive quantities Ai, i = 1, . . . , M, that characterize the context one is working with.