From NIST SP 800 - 90A from January 2012 (see http://csrc.nist.gov/publications/nistpubs/800-90A/SP800-90A.pdf), page 6:
For the purposes of this Recommendation, an n-bit string is said to have full entropy if that bit string is estimated to contain at least $(1-\epsilon) n$ bits of entropy, where $0 <= \epsilon <= 2^{-64}$.
My understanding of entropy is that entropy is a property of the probability distribution of a source of bit strings, and not a property of a single bit string.
So what is NIST specifying here? Is there a way to estimate the entropy of the underlying source, given a bit string produced by that source? Maybe statistical tests, like Maurer's universal test? This could only be probabilistic since in principle, a true source of randomness can create any bit string...