We know that algorithms have a certain space and time complexity when implemented. Optimizing algorithms often involves a space-time tradeoff, where one increases space used in exchange for a decrease in time.
However, based on conservation of energy, and the equivalence of spacetime, are space-time tradeoffs in any way related? The energy saved by reducing runtime is instead spent in holding more items in memory, for example. (I know it's possible to have a bad algorithm that increases space and time always, but I am talking in the context of optimization.
Is there any way we can quantify this based on mathematical formulae?