Abstract: In the last few years, there has been a wave of interest in thermodynamics of very small or strongly correlated systems. This research, rooted in quantum information theory, has given rise to several interesting mathematical questions on majorization and its behavior under tensor products. In the talk, I will present one theorem that concerns majorization of probability distributions under the creation of correlations in auxiliary systems. As a by-product, we obtain a characterization of Shannon entropy as the essentially unique real function on probability distributions which is Schur-concave, additive, and subadditive.