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The Physics of Energy Flow – No Sources or Sinks

2026-03-11

# 4. No Sources or Sinks Across the extent of $u$, continuity holds. Energy transported across a region does not create or destroy energy there. Rather, it changes how much energy is stored there by moving it across regions. Since $u$ is what is given to exist, its total quantity is given with it and can therefore be considered fixed. A primitive source or sink would require either that total to change or that disconnected regions compensate one another without transport between them. This is the source-free continuity statement itself: no added creation term, no added destruction term, only transport. Continuity gives local accounting. We now explore what it implies for the shape of energy reorganization as a complete process. Although $\mathbf{S}$ handles a directional accounting of how energy is transported, even when taken as a whole it still fails to reveal the structure of that transport. The next chapters develop that structure. We next consider the transport of energy across empty space.
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