It is generally assumed that the thermodynamic stability of equilibrium state
is reflected by the concavity of entropy. We inquire, in the microcanonical
picture, on the validity of this statement for systems described by the
bi-parametric entropy Sκ,r​​ of Sharma-Taneja-Mittal. We analyze
the ``composability'' rule for two statistically independent systems, A and B,
described by the entropy Sκ,r​​ with the same set of the deformed
parameters. It is shown that, in spite of the concavity of the entropy, the
``composability'' rule modifies the thermodynamic stability conditions of the
equilibrium state. Depending on the values assumed by the deformed parameters,
when the relation Sκ,r​​(A∪B)>Sκ,r​​(A)+Sκ,r​​(B) holds (super-additive systems), the concavity
conditions does imply the thermodynamics stability. Otherwise, when the
relation Sκ,r​​(A∪B)<Sκ,r​​(A)+Sκ,r​​(B) holds (sub-additive systems), the concavity
conditions does not imply the thermodynamical stability of the equilibrium
state.Comment: 13 pages, two columns, 1 figure, RevTex4, version accepted on PR