Information exchange in causally non-separable processes

For a system of two parties, the process matrix framework predicts existence causally non-separable structures. Our objective is to provide general condition for identifying such indefinite causal order in terms mutual information exchange. In detail, we show that there are processes which total entropy parties greater than one any separable with same non-signaling part. Furthermore, this not satisfied all processes, particular at least some do violate inequalities.