Detecting the amount of entropy used for random number generation I am majoring in computer science but I have recently become obsessively interested in information theory and cryptography. I have read some articles about entropy and random number generators. 

I find few algorithms online to generate 128-bit entropy supported random number generator. As I can tell from other discussion in this website that random number generator does not change the entropy.

It seems that N-bit-entropy-support random number generator only depends on how many bit of initial state supported by the algorithm. If my understanding is correct, I wonder if it is possible to figure out the how many bit of entropy supported by any given random number generator if we don't know the algorithm (like testing it in a black box)?
Suppose we have some seed-extensible PRG, meaning, it can operate on seed of any length $l$, and extracts a pseudorandom string in time polynomial in $l$ and the output length. What you are asking is: given a pseudorandom string produced by this PRG, can I find the input length $l$ that was chosen?

The number of bits of entropy fed as seed to a cryptographic pseudorandom generator can be seen as the security parameter $\lambda$ for the system. The security of your PRG (assuming it is a cryptographically strong PRG) states that any adversary that runs in time polynomial in $\lambda$ cannot distinguish the pseudorandom output from a random string. In particular, if it cannot distinguish it from a random string, it cannot tell anything at all about the input length that generated it. Therefore, either you have chosen $\lambda$ so that breaking the security of the PRG takes too much time for the adversary, and he will in this case not be able to tell the seed length either, or you have set up $\lambda$ to be a too small value, in which case the adversary will indeed find out the seed length, but also break the security of your PRG.