  After Shannon, entropy becomes a fundamental quantity to describe not only
uncertainity or chaos of a system but also information carried by the system.
Shannon's important discovery is to give a mathematical expression of the
mutual entropy (information), information transmitted from an input system to
an output system, by which communication processes could be analyzed on the
stage of mathematical science. In this paper, first we review the quantum
mutual entropy and discuss its uses in quantum information theory, and secondly
we show how the classical mutual entropy can be used to analyze genomes, in
particular, those of HIV.
