How much entropy is lost via hashing when you add known or low entropy data?
A simple way to imagine the effect of the hash function is a truncation. A "good" hash function ought to behave like a random oracle. If your source has entropy $s$ bits, then this means that the source somehow assumes $2^s$ possible values. When processed with a random oracle with an $n$-bit output, you force the $2^s$ input values into $2^n$ possible outputs.

When $s$ is smaller than $n/2$, then it is expected that the hash function will produce $2^s$ distinct values, and all your $s$ bits of entropy are preserved. When $s$ reaches $n/2$, collisions begin to appear, and each collision means a tiny fraction lost entropy. You still preserve most of it, though. When $s$ reaches $n$ (e.g. you hash an input with 256 bits of entropy, with SHA-256), then it is expected that you get about $0.6·2^s$ distinct output (you lost one third of the inputs to collisions), so the resulting entropy will be a bit more than $n - 1$ bits. When $s$ is higher than $n$, the output entropy will still rise, but never exceed $2^n$: you cannot have more than $2^n$ distinct outputs of $n$ bits...

To sum up, when hashing your input, you preserve almost all your input entropy, up to at most the output size of the hash function. To make things simple: when you hash with SHA-256 an input of entropy $s$ bits, then you get an output entropy at least equal to the lower of $s-1$ and 255 bits.