Looking at the Earth system as a whole and considering ecological economics, net primary productivity and emergy are two concepts that strike me as fundamental and likely related. I'm not sure what the relationship is though.
I'd define emergy as embodied energy, or how much total gross joules are embodied in a given process or material (or organism).
I'd define net primary production as the total mass of organic compounds synthesized from "inorganic carbon" (primarily atmospheric carbon dioxide). While this metric is a mass, it also sheds light on how relatively efficiently solar energy is used to generate life (or at least the ingredients of life, "organic" carbon compounds).
At first these two metrics seem quite different: one is a measure of energy, one is a mass. However, both metrics clarify the relationship between our relatively open-system energy resource and our closed-system nutrient cycles. For example, I in comparing different agroecosystems growing an apple, emergy can help show the energetic efficiency of each system and net primary production can help show the life-generating efficiency of each system. My word choices there seem a little ambiguous, for example, what's the difference between "energetic efficiency" and "life-generating efficiency"? That's what spurs the main question, which is: what, if any, is the relationship between net primary productivity and emergy?
Clarification about the qualitative relationship between the two metrics would be helpful, I understand it may be overly complex to quantify it though the two terms are very much quantitative. Researching this I've found plenty of resources about each metric but none yet comparing the two, so any resources simply comparing the two would be an answer/step in the right direction.