Encrypted data should be statistically indistinct from random noise.
It's an information theory thing. Everything in the ciphertext should be sitting at maximum entropy.
There are even statistically measurable differences in the garbage written across versions of a tool or OS, which, unlike the invented scenario above, has been successfully used to place a time window on when exactly someone destroyed evidence.
"Garbage" isn't the same thing as random noise.
I have looked at the entropy graphs of encrypted data commonly. It's one of the first things I look at when looking at a new firmware image I haven't seen before.
Merely that, unlike in the invented scenario above, statistical differences in the random garbage that gets written to a disk across different tool or OS versions has been successfully used to place a time window on when exactly someone destroyed evidence.
A LUKS volume with a detached header is indistinguishable from random data.
Compare the entropy graph of /dev/random against a LUKS volume with a decrypted header, and you will see no difference.