The non-conditional nature of the Cerf-Adami inequalities and   implications for thermodynamics
  We show that the Cerf-Adami inequalities do not necessarily depend on conditional entropies nor any reference to Markov chains. While the latter are not explicit in the original form, they are often implied in certain derivations. We also show that these inequalities are intimately related to at least one interpretation of the second law of thermodynamics. The combination of these results provides added insight into why some quantum systems violate the Cerf-Adami inequalities thereby improving our understanding of the quantum-classical boundary. As a result we suggest that the second law may serve as some type of boundary condition on classical knowledge. 
Ian T. Durham