What is the entropy of a random sequence of N elements in an interval containing S terms?

Question

The NSA is always hunting down their next generation of employees. Since the entropy of a string of symbols chosen randomly from a set of N symbols is a measurable quantity, somebody must be able to wed physics with set theory and combinatorics permutations to obtain a spectral percent answer of the amount of chaos or order within a quantity of information. The amount of energy required to restore order to a given piece of information is highly related to brute force algebraic attacks by computers operating at C cycles per second. If there is no algorithm that restores order, then the amount of energy required is the sum of every algebraic calculation to check every solution in the set of all solutions. Similar to the library of Babel and a reference system to check out only one book. How do you identify a single book out of all possible books without the same quantity of information contained in the book you desire to check out?