This section defines some terms and notation that will be used freely in later sections. The list of definitions given below is ordered so that each definition only uses terms that have been defined in previous definitions.
S = -[p_{1} log_{2}(p_{1}) + p_{2} log_{2}(p_{2}) + ... + p_{D} log_{2}(p_{D})].
For example, if all p_{i} are equal to 1/D, this gives S=log_{2}(D). D is the number of states or degeneracy of the distribution. If D = 2^{B} (B is referred to as the number of bits), then S = B.
As another example, suppose that one p_{i} equals one and all others equal zero. Then, S=0 (because log1=0, and xlog(x) tends to 0 as x tends to 0 with x>0.)
In general, one can show that 0<= S <= log_{2}(D) so the two examples just given represent the two extremes.
You can think of S as measuring the spread (dispersion) of the distribution.
Some of the above definitions may not make sense to you the first time you read them. Don't worry. You'll understand them better as you learn more about Quantum Fog.
Congratulations! You've just endured one of the hardest parts of this manual. And now for a fun part.
We suggest that next you read the section entitled "Quick Tour".