Check out my new paper:
“Some Quantum Information Inequalities from a Quantum Bayesian Networks Perspective”, by Robert R. Tucci, arXiv:1208.1503 (abstract here)
the inequalities of SIT (Shannon Information Theory) and of Thermodynamics (e.g. that minor inequality )
and then there are
and never the twain shall meet?
Of course not.
In classical SIT, a well known inequality is the so called Data Processing Inequality which says that any Markov chain
In other words, the correlation between and is larger than the correlation between and node , which is more distant from than node .
But a Markov Chain is just a super simple network. Why stop there? Why not consider more complicated networks? And why limit yourself to classical SIT. Why not quantum SIT too? See my new paper for a pedagogical introduction to the secret romance between SIT and Bayesian networks, a romance which goes on in both classical and quantum physics.