Ideal gas provides -entropy

A mathematical procedure is suggested to obtain deformed entropy formulas of type K ( S K ) = ∑ 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 Rényi and Tsallis formulas. A novel interpretation of the q ∗ = 2 − q duality arises from the comparison of canonical subsystem and total microcanonical partition approaches. In the sequel a new, generalized deformed entropy formula is constructed for the linear C ( S ) = C 0 + C 1 S relation.