Why link me to the Wikipedia article or insinuate I'm pulling this out of--to put it more politely--ex culo? Given my use of notation, one might assume I am at least a little familiar with how the thermodynamic entropy functions are mathematically derived.
To be pedantic for a bit, Entropy is an abstract mathematical state function useful for the prediction of thermodynamic systems. Much like the Gibbs and Helmholtz terms, entropy has no direct qualitative basis; there are many open-ended interpretations seeking to justify what it means, which is not unlike looking for God or faeries or what have you.
Mathematically speaking, I think you got your equality / definition wrong. Which energy function do you refer to? If you are still convinced about an error on my part, you can demonstrate in classical thermodynamics that,
S = "the inverse of available energy to do anything"