From Thermodynamic Sufficiency to Information Causality

The principle called information causality has been used to deduce Tsirelson's bound. In this paper we derive information causality from monotonicity of divergence and relate it to more basic principles related to measurements on thermodynamic systems. This principle is more fundamental in the sense that it can be formulated for both unipartite systems and multipartite systems while information causality is only defined for multipartite systems. Thermodynamic sufficiency is a strong condition that put severe restrictions to shape of the state space to an extend that we conjecture that under very weak regularity conditions it can be used to deduce the complex Hilbert space formalism of quantum theory. Since the notion of sufficiency is relevant for all convex optimization problems there are many examples where it does not apply.