Qualified no. There is no relationship between source entropy and the output entropy from a TRNG other than you can't output more entropy than you put in. The actual source entropy rate can vary vastly. Clearly the TRNG output entropy has to be 100%, 1 bit /bit or however you measure it. Otherwise it wouldn't be a TRNG with a statistically flat output.
I like to talk in percentages, with 100% being absolute true randomness. A physical source can produce entropy at any rate from 0 - 100%. I can't imagine a physical source that can naturally produce 100% though. I have built two generators that produce entropy at the rates of 85% and 1.9%. An experimental third outputs at a very very approximate 0.1%.
It's all to do with what happens to the source entropy once you've digitised it. I think of entropy extraction as a distillation process akin to whiskey production. The distillation process is a euphemism for lossy compression of the source entropy. This might be a (non) cryptographic hash, matrix multiplication or just some simple bit folding. Most TRNG devices use custom extraction techniques anyway.
If you start with 85% mash, you only need to refine /compress the mash /entropy by 17% to get 100% pure stuff. Similarly the compression /refinement needs to be 52 fold for the 1.9% mash. So 52 fold compression would result in a 100% rate of entropy. But then consider that you might continue compression /refinement, so in the end you've compressed the 1.9% source entropy 100 fold. Or 200 fold. You still get 100% output entropy and the numbers are exactly just as random. This is why there is no particular relationship between the source entropy and the output of a TRNG.
