Marginal Polytope of a Deformed Exponential Family

A deformed logarithm function called $q$-logarithm has received considerable attention by physicist after its introduction by C. Tsallis. J. Naudts has proposed a generalization called $\phi$-logarithm and he has derived the basic properties of $\phi$-exponential families. In this paper we study the related notion of marginal polytope in the case of a finite state space.