The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive entropies. This limits the range of the nonextensivity parameter $q$ to $\left(0,1\right)$ so as to preserve the concavity of the entropies. The Tsallis entropy is thereby found to be appropriately renormalized.

• Received 22 March 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.1711