On the energetic boundaries of trophic systems

Energy is the fundamental currency of life. Every organism requires a minimum intake to meet maintenance needs, and every trophic transfer dissipates part of the energy flow as heat. Classical theory has emphasized lower bounds on supply--the minimum resource level required for consumers to persist--yet the possible upper bounds and their role in limiting food-chain length remain unclear. We develop a thermodynamically grounded framework that reveals a triad of boundaries: (i) consumer thresholds, (ii) a basal protection limit that reframes the paradox of enrichment as a thermodynamic constraint, and (iii) environmental or physiological supply caps. We show that the intersection of these three boundaries determines the exact range of conditions under which a given ecosystem structure can occur, and that within this range trophic configurations arise as the unique solution that maximizes energy flow. As chain length increases, consumer thresholds rise while the basal protection limit falls, causing this range to contract and eventually disappear. Whether this limit is reached depends on the relative position of these two boundaries and the external supply cap. Their crossing defines an energetic ceiling: a thermodynamic bound on food-chain length beyond which no further level can be sustained. Our results show that feasibility conditions are directly shaped by thermodynamic laws, providing a mechanistic explanation for the emergence and limits of trophic systems.