  We introduce a binary relation on the finite discrete probability
distributions which generalizes notions of majorization that have been studied
in quantum information theory. Motivated by questions in thermodynamics, our
relation describes the transitions induced by bistochastic maps in the presence
of additional auxiliary systems which may become correlated in the process. We
show that this relation is completely characterized by Shannon entropy H, which
yields an interpretation of H in resource-theoretic terms, and admits a
particularly simple proof of a known characterization of H in terms of natural
information-theoretic properties.
