There is no particular correlation between value creation and energy consumption. Your theory is likely unique. I could burn a log, releasing a lot of energy, and no value would be created. I could carve a figure into a log and create value.
Your examples disagree with your initial statement actually. How did you get the log? How did you carve the figure? Both of these require energy consumption, as we aren't at the stage where we are magically planting trees and teleporting them into our workspaces for carving/burning.
Take away all energy from this world. You get 0 value creation. Everything is dead nothing can move.
That’s the correlation. I don’t understand why you’re using big words like correlation as if this is something that needs to be studied. It’s common sense imo.