**13. The Entropy of a Code with
Probabilities**

The entropy of a code with probabilities is defined and as a consequence
the concept

of conservation of entropy in lossless coding emerges in a natural manner.

For any given probability distribution (p1, p2,…pT) all the distinct decompositions

of the associated entropy function h(p1,p2,…,pT), as a function of entropies
of lower orders,

are obtained from the terminal uncertainty of the distinct rooted trees
with leaf probabilities

(p1,p2,…pT).