Thermodynamic equilibrium and its stability for microcanonical systems described by the Sharma-Taneja-Mittal entropy

It is generally assumed that the thermodynamic stability of equilibrium states is reflected by the concavity ofentropy. We inquire, in the microcanonical picture, about the validity of this statement for systems described bythe two-parametric entropy S,r of Sharma, Taneja, and Mittal. We analyze the "composability" rule for twostatistically independent systems A and B, described by the entropy S,r with the same set of the deformationparameters. It is shown that, in spite of the concavity of the entropy, the "composability" rule modifies thethermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformationparameters, when the relation Sk,r(AB)>Sk,r(A)+Sk,r(B) holds (superadditive systems), the concavitycondition does imply thermodynamics stability. Otherwise, when the relation Sk,r(AB)