Is there an idea of entropic potential energy/gradient/pressure? Could you differentiate encrypted data from noise by testing how much energy it requires to flip a bit?
No, because the energy of the system isn't related to the order of the underlying data, it's related to the changes that happen to the underlying data. If you have 5 bits and flip 3, it takes the same energy regardless of if the 5 bits have meaning or not. This is speaking in terms of physics. There obviously could be some sort of practical side channel attack based on error checking times if this was an actual processor.
Only if you were measuring a system with access to the key material and doing something with the plaintext, in which case this would be a side-channel attack (and an already-studied one). The whole point of encryption is that the data output is indistinguishable from noise without knowing the key.
