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An energy flow diagram is normally a flow diagram showing the energy gains and energy losses of a given process. This type of diagram is often used to show the efficiency of a given system or lack thereof.
A swinging unpowered pendulum would maintain the same rate between the swings as it slowed down. Like a bell the frequency remains the same but the amplitude reduces as it quiets.
The arrows point to the thing that eats it, for example on an arctic marine food chain, the polar cod would have the arrow pointing into the narwhal, because the narwhal gets the energy