The non-conditional nature of the Cerf-Adami inequalities and implications for thermodynamics

TL;DR

This paper demonstrates that Cerf-Adami inequalities are inherently non-conditional and explores their connection to thermodynamics, offering insights into quantum violations and the classical-quantum boundary.

Contribution

It reveals that Cerf-Adami inequalities do not rely on conditional entropies or Markov chains and links them to the second law of thermodynamics.

Findings

Cerf-Adami inequalities are non-conditional.

These inequalities relate to the second law of thermodynamics.

Quantum systems can violate these inequalities.

Abstract

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.