  For noncomposite systems in classical and quantum domains, we obtain new
inequalities such as the subadditivity and strong subadditivity conditions for
Shannon entropies and information determined by the probability distributions
and for von Neumann entropies of quantum states determined by the density
operators. We extend the relations of Shannon and Tsallis entropies to the
entropies of conditional probability distributions known for composite systems
to the case of noncomposite systems. We give a review of the approach to
construct the tomographic-probability distributions for qudit systems and
present the entropic and information inequalities for spin tomograms, as well
as the subadditivity and strong subadditivity conditions for tomograms of the
both noncomposite and composite system states.
