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Matter/energy can neither be created nor destroyed. So in a given volume, there's a finite amount of energy, whether it be kinetic or potential, at any given moment.
So, would increased activity in one area result in lower energy, or decreased activity in another? Of course energy is recycled, but only so much action can take place, universe-wide, in any given moment. If you consciously engage in more activity than you might have otherwise, perhaps you really are "stealing time", "seizing the moment" or "getting a bigger piece of the action".
If a moment is a quantum unit of time (in laymen's terms), it's value is proportional (somehow, I'll let more competent folk work the math if you wish), to the total amount of matter/energy within the observed volume.
I don't know if that's a new idea, but it's new to me.
There is practically no connection between the amount of matter/energy within an observed volume and the rate of time within the same volume unless you go to relativistic extremes. Increased activity in one area can come from the conversion of potential energy to kinetic as in the example of a fire or from the conversion of matter to energy as with a nuclear explosion. Or you could have something like a melting ice cube where the ice warms as it absorbs energy from the air. Here you have an increase in energy in one area and a simultaneous decrease in energy in another.
I have a feeling I may have misunderstood your question and you have something else in mind.
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