The answer to your question is not straightforward, but it is not a definite "no". Here is an interesting (albeit amateur) discussion on the subject on Stack Exchange: https://cs.stackexchange.com/questions/26049/is-there-a-conn...

This is in relation to the ‘say more’ part, not specifically about the halting problem or P/NP.

Since computation is physical, there are theoretical bounds on the energy consumption of computation. (Landauer’s principle [0]).

Physical limits computation are at least one way to think about the relationship between thermodynamics and software.

[0] https://en.m.wikipedia.org/wiki/Landauer%27s_principle