In the multitude of those daily and monthly and yearly cycles of reproduction in which an empire regenerates itself, there is a sort of principle of diminishing net energy return that could be generalized and scaled out.
An empire is constantly simultaneously damaging itself as it shores itself up and takes energy into itself. The instruments of violence it unleashes to shape its world and the Others in its world are not easily contained, and are perpetually turned back on itself as it operates.
When one sets upon the land and terrorizes it to mass produce a monocultured crop for instance, one is also extinguishing the dynamic life in the soil, and the soil yields less and less over time, and the problem is moved spatially or technologically for the time being, whether by seeking more soil or artificially shoring up the soil with fertilizer say.
And one may vanquish an enemy and rival, but the memory of that violence never quite goes away, whether that memory is in the crushed rival or in the victor itself. Just because the destruction moves does not mean it goes away.
Soon enough that destruction - like the concentrated energy on the other side of that coin - pools and concentrates, and so moves things in accordance with its own logic.
Rome continued to weaken in part because its enemies learned and grew stronger at the same time that Rome forgot and grew weaker, and those trajectories would pass each other and eventually reach a tipping point: one could see in the history that just as late imperial Rome was achieving stability again after a time of trouble, and beginning to heal itself and regenerate itself, there would be some new invasion, or another flaring civil war, a delayed effect from its previous troubles, and it would be thrown back into the dynamics of its downward spiral.
At some point, all of the many cycles of reproduction required to sustain such a continuity begin to lose their buoyancy and vitality, as the energy produced from them is not to operate the cycles themselves, much less encourage any more expansion or to break even for that matter.
