Majorization is a well-studied partial order in information theory and matrix analysis, known for its versatility and broad applications. In recent years, it has become increasingly significant in quantum information theory as well. This talk will explore generalizations of this partial order, specifically to joint probability distributions and classical channels. We will also discuss how these concepts extend to the quantum realm, leading to profound results. In particular, we will present our recent findings on the inherent negativity of quantum channel entropy and offer new insights into the relationship between quantum channels and bipartite correlated systems. Advisor: Prof. Gilad Gour