On the energetic boundaries of trophic systems
Bibliographic record
Abstract
Abstract 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".