Ideal gas provides q-entropy

A mathematical procedure is suggested to obtain deformed entropy formulas of type K(SK)=∑PiK(−lnPi), by requiring zero mutual K(SK)-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)=C0+C1S relation.