formula.

Generalized, nonadditive entropy definitions has been investigated in various problems from high energy physics [@B1] to DNA analysis [@DNA], and it has been a longstanding problem that the zeroth law of thermodynamics (i.e. the existence of a well defined temperature function in thermal equilibrium) cannot be compatible with nonadditive entropy composition rules. A possible resolution to this problem has been proposed recently by Biró and Ván in [@PhysRevE.83.061147], where they developed a formulation to determine the most general functional form of those nonadditive entropy composition rules that are compatible with the zeroth law of thermodynamics. They found that the general form is additive for the *formal logarithms* of the original quantities, which in turn, also satisfy the familiar relations of standard thermodynamics. In particular, for homogeneous systems, they showed that the most general, zeroth law compatible entropy function takes the form $$\label{eq:formallog}
L(S)=\frac{1}{\lambda}\ln[1+\lambda H_{\lambda}(S)],$$ which is additive for composition, i.e., $$L(S_{12})=L(S_{1})+L(S_{2}),$$ and the corresponding zeroth law compatible temperature function can be obtained as $$\frac{1}{T}=\frac{\partial L(S(E))}{\partial E},$$ where $E$ is the energy of the system.

In the case of the Tsallis statistics, it is easy to show that by taking the formal logarithm (\[eq:formallog\]) of the Tsallis entropy (\[TsS\]), i.e. 