Ideal gas provides qq-entropy

• It is shown that for a finite, energy independent heat capacity ideal gas the additive quantity is the qq-entropy.
• For a canonical subsystem energy-distribution with the same procedure a dual, 2−q2−q, entropy formula emerges.
• Additivity for a general heat capacity reservoir defines a more general entropy formula.
• This additivity can be formulated as a universal thermostat independence principle.
• For linear heat capacity–entropy relations the entropy formula is constructed.

A mathematical procedure is suggested to obtain deformed entropy formulas of type K(SK)=∑PiK(−lnPi)K(SK)=∑PiK(−lnPi), by requiring zero mutual K(SK)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, CC, where it delivers the Rényi and Tsallis formulas. A novel interpretation of the q∗=2−qq∗=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+C1SC(S)=C0+C1S relation.