We review the concept of majorization and its relation with generalized information
measures. Majorization theory provides an elegant framework for comparing two probability
distributions, leading to a rigorous concept of disorder which is more stringent
than that based on the Shannon entropy. Nevertheless, it is shown that it can be fully
captured through general entropic inequalities based on generalized entropic forms. A
brief review of generalized entropies is also provided. As illustration, we discuss the
majorization properties of generalized thermal distributions derived from generalized
entropies, and identify rigorous mixing parameters. We also describe majorization in
quantum systems. We discuss in particular its capability for providing a disorder based
criterion for the detection of quantum entanglement, which is stronger than that based
on the von Neumann entropy and leads to a generalized entropic separability criterion.
Keywords: Generalized Entropies, Majorization, Generalized Thermal Distributions,
Mixing Parameters, Quantum Mixed States, Quantum Entanglement, Separability.
