  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.
