Zeroth Law compatibility of non-additive thermodynamics

Understand

Non-extensive thermodynamics was criticized among others by stating that the Zeroth Law cannot be satisfied with non-additive composition rules.

• In this paper we determine the general functional form of those non-additive composition rules which are compatible with the Zeroth Law of thermodynamics.
• We find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these.
• Our result offers a possible solution to the longstanding problem about equilibrium between extensive and non-extensive systems or systems with different non-extensivity parameters.