  We discuss that the thermodynamical Legendre transform structure can be
retained not only for the arbitrary entropic form but also for the arbitrary
form of the energy constraints by following the discussion of Plastino and
Plastino. The thermodynamic relation between the expectation values and the
conjugate Lagrange multipliers are seen to be universal. Furthermore, Gibbs'
fundamental equation is shown to be unaffected by the choice of the entropy and
the definition of the mean values due to the robustness of the Legendre
transform structure.
