  A mathematical procedure is suggested to obtain deformed entropy formulas of
type K(S_K) = sum_i P_i K(-ln P_i), by requiring zero mutual K(S_K)-information
between a finite subsystem and a finite reservoir. The use of this method is
first demonstrated on the ideal gas equation of state with finite constant heat
capacity, C, where it delivers the Renyi and Tsallis formulas. A novel
interpretation of the qstar = 2-q duality arises from the comparison of
canonical subsystem and total microcanonical partition approaches. Finally a
new, generalized deformed entropy formula is constructed for the linear
relation C(S) = C_0 + C_1 S.
