Does Landauer's principle not already create a very strong link between the two? https://en.wikipedia.org/wiki/Landauer%27s_principle

It even predicts a direct equivalence between the unit of bit and Joules per Kelvin with the entropy produced in the erasure of a bit being equal to 9.6e-24 J/K

Unless I'm making some mistake, you can even use computer science principles combined with Landauer's limit to solve Maxwell's Demon.