Conditional Information Inequalities for Entropic and Almost Entropic   Points
  We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be extended to any unconditional linear inequalities. Some of these conditional inequalities hold for almost entropic points, while others do not. We also discuss some counterparts of conditional information inequalities for Kolmogorov complexity. 
Tarik Kaced and Andrei Romashchenko
cs.IT cs.DM math.IT math.PR