I don't know if it will work on something as small as a private key, but you can compress the key. If the compressed key is significantly smaller then the original, it lacks entropy. Pure random data is mostly incompressible.
Note that 32 0x00 is a possible output from a pure random generator while still being quite compressible, you would probably still want to throw that one out though. After buying a lottery ticket.
Note that 32 0x00 is a possible output from a pure random generator while still being quite compressible, you would probably still want to throw that one out though. After buying a lottery ticket.