Functional Stability Theory II: Chemical Stability and Autocatalytic Selection

A game-theoretic framework for prebiotic chemistry, interpreting autocatalytic networks, hypercycles, and chirality selection as Nash-equilibrium-like structures of thermodynamic games.

Building on Dynamic Kinetic Stability (DKS) and the England inequality, we propose that the Maximum Entropy Production Principle (MEPP) serves as a stability filter—demarcating the viable manifold of replicating systems—rather than as a causal driver. Empirical motivation comes from Azoarcus ribozyme experiments, where RNA replication dynamics conform to classical payoff matrices (cooperation, dominance, Prisoner's Dilemma). Homochirality is modeled as spontaneous symmetry breaking in a degenerate Nash equilibrium. The framework explicitly treats MEPP as contested far from equilibrium and separates known chemical kinetics from the proposed game-theoretic reinterpretation.

Series position

FST-II is the chemistry / autocatalytic stability companion (Level 1b) of the FST application series. The programmatic umbrella is the FST Hub (Concept-DOI 10.5281/zenodo.20130499). Sibling application companions: FST-I Thermodynamic Stability, FST-III Biological Stability, and FST-IV Cosmology.

Code & sources

GitHub: research-line/functional-stability-theory / applications/fst-ii-chemical.

Version 1.5 (June 2026)

• Measurement-gate ledger: the English and German papers now include a prediction/measurement ledger before P1--P6, separating each target prediction from independent observables and the current validation gate.
• Citation and bibliography maintenance: the English and German bibliography order was synchronized, 21 confirmed DOI-capable references were supplemented, and the Swenson 1989 reference was corrected to the complete Crossref title.
• DOI verification: 39/39 unique DOI handles resolve through the DOI registry; English and German citation, bibliography-item and DOI sets are identical.
• Files rebuilt locally: English, German and combined bilingual PDFs were rebuilt on 2026-06-04 after the post-v1.4 data/structure, citation and source-check maintenance passes.

Version 1.6 (June 2026)

• Claim-guardrail maintenance: the Pattern-A/RH bridge is now explicitly an optional structural analogy, not a chemical rank or positivity theorem.
• Thermodynamic framing: the England-bound discussion now treats the bound as a thermodynamic viability condition rather than a Jacobi or resolvent instability certificate; dynamic elimination requires an explicit kinetic model.
• Scope calibration: DESS, homochirality, P4/P5 and MEPP passages were tightened to regime- and model-dependent claims, with Frank-/Viedma-type mechanisms and reaction-diffusion assumptions stated explicitly.
• PDF-design maintenance: the English and German sources now use lmodern/glyphtounicode; the German PDF text layer preserves real umlauts, a broken prisoner-dilemma table line was repaired, and the English status table was polished.
• Files rebuilt locally: English, German and combined bilingual PDFs were rebuilt on 2026-06-13 after the strict-review and PDF-design maintenance passes.

Changelog

Version 1.4 (May 2026)

• Proof/paper synchronization: the England-bound discussion now uses the Jensen consequence directly and avoids the earlier misleading exponential-average shorthand.
• Stability guardrail: the stability boundary is described through spectral abscissa on the relevant tangent/stoichiometric subspace; spectral radius remains only a stiffness or oscillation proxy.
• Replicator boundary cases: boundary rest points and Nash equilibria are separated more carefully; absent species with neutral or positive invasion channels prevent asymptotic-stability claims.
• Script and result hygiene: `autocatalysis_3species.py`, `replicator_entropy_test.py`, `ii_calc_01_results.json`, and public replicator result JSONs now carry the same guardrail language as the paper.
• Citation maintenance: active EN/DE bibliographies were rechecked; DOI fields for England, Crooks, MEPP, Metabolic Nash, Kauffman and Schuster et al. were corrected or completed.
• Files rebuilt and synced: English, German and combined bilingual PDFs were rebuilt and the public GitHub package was synchronized to the same post-v1.3 guardrail file set.

Version 1.3 (May 2026)

• Strict-review guardrails: Three-species stability example now distinguishes the neutral mass-conservation mode from tangent-space asymptotic stability.
• Claim calibration: The spectral radius is framed as a local stiffness/oscillation proxy, not as distance to a stability boundary.
• P3 calibration: The replicator table is framed as a catalytic-throughput toy proxy, not as independent entropy-production evidence.
• DE/EN synchronization: German DESS, Boerlijst/Hogeweg, homochirality, and MEPP wording aligned to the more cautious English claim level.

Version 1.2 (May 2026)

• Source correction: FST-I self-citation corrected from unrelated Zenodo record DOI 10.5281/zenodo.14920522 to the FST-I concept DOI 10.5281/zenodo.20130544.
• Source correction: RH/RFEP self-citations corrected from unrelated Zenodo record DOI 10.5281/zenodo.15076553 to the RH and RFEP concept DOIs 10.5281/zenodo.19035640 and 10.5281/zenodo.19036190.
• Bibliography cleanup: Harper arXiv note no longer claims an unverified Journal of Theoretical Biology version; ChemSystemsChem article data and several DOI fields were aligned with Crossref, PubMed, and Zenodo checks.
• Claim calibration: England's inequality is framed as a constraint/consequence rather than a causal driver; MEPP is treated as a heuristic stability filter, not as a proven selection law.
• Minor-revision response: The paper now distinguishes established kinetics from the FST-II game-theoretic synthesis and includes a concrete experiment distinguishing FST-II from standard kinetic dominance predictions.
• Files: This release contains English, German, and combined bilingual PDFs.

Version 1.1 (May 2026)

• Hub-link corrected: "FST-IV Overview" references replaced by "FST Hub" (programmatic umbrella). The Hub paper holds Concept-DOI 10.5281/zenodo.20130499 and is no-numeral; FST-IV is now the cosmological collector slot.
• GitHub source link added.
• Related Identifier: FST-DE reference relabelled to "FST-IV Cosmology / FST-DE".

Version 1.0 (May 2026)

• Initial release as part of the FST series. Status: ~8.5/10 readiness; remaining open items per referee minor-revision verdict: MEPP-controversy framing, England-causal weakening, distinction known-kinetics vs. new game-theory insights, additional experimental tests.