Is there any correlation between heat death and zero point energy?

Answer 1

The short answer is simple: no.

The more advanced answer is this: the two have very little to do with each other.

"Heat death" is a concept first proposed by William Thomson (aka Lord Kelvin). It surmises that our Universe will eventually reach a point of complete thermal equilibrium, a time after which no energy can be transferred from one point to another. Thus, no motion, and certainly no life, could exist. The idea is now discredited due to our knowledge of black holes, which make such an equilibrium impossible -- a large chunk of matter in our Universe will eventually end up in these objects, thus preventing much exchange of thermal energy between them. Thus, these objects never reach thermal equilibrium between each other. Thus, it is a concept based on thermodynamics, discredited due to general relativity.

Zero point energy is a fact of our Universe that nothing in our Universe -- not even space completely devoid of matter -- can ever be at a zero energy level. Quantum mechanics requires that some energy MUST exist everywhere. The fact that some energy does exist in (otherwise) empty space has certain implications that can be experiementally measured -- these experiments have been carried out, and the results agree with the predictions of zero point energy. This scientific fact is based on quantum mechanics, and has no connection to either thermodynamics or general relativity.