Measurement entropy in generalized nonsignalling theory cannot detect bipartite nonlocality

We consider entropy in generalized nonsignalling theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a bipartite state. We find that the only inequalities among these entropies are subadditivity and non-negativity. Surprisingly nonlocality does not play a role—in fact, any bipartite entropy vector can be achieved by separable states of the theory. This is in stark contrast to the case of the von Neumann entropy in quantum theory, where only entangled states satisfy $S\left(AB\right)<S\left(A\right)$.