# Chemical Systems as Ternary $\\Gamma$-Semirings:Theory, Case Studies, and Operational Tests

Source: [Chemical Systems as Ternary $\\Gamma$-Semirings:Theory, Case Studies, and Operational Tests](<https://www.sota2.com/research/paper/6923e69ad6b0dd334292f097>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-25T05:03:07.149Z

Authors: Chandrasekhar Gokavarapu, Rajahmundry, Andhra Pradesh, India and, Department of Mathematics, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India), Venkata Rao Kaviti, Rajahmundry, Andhra Pradesh, India), Srinivasa Rao Thirunagari, Rajahmundry, Andhra Pradesh, India), D. Madhusudhana Rao, Guntur, Andhra Pradesh, India and, Department of Mathematics, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India)

Published: 2025-11-17T18:29:31.000Z

## Abstract

Chemical systems are traditionally described by lists of species, reactions, and externally imposed kinetic laws, a framework that lacks an intrinsic algebraic structure governing how transformations compose. We propose an axiomatic reformulation in which a chemical system is modelled as a ternary Gamma semiring (TGS), where chemical states form an additive semigroup, mediators encode catalytic or environmental context, and mediated transformations are represented by a ternary operation. We show that the TGS axioms admit direct physical interpretations: distributivity corresponds to ideal, non-interfering parallel reactions, while associativity characterizes thermodynamic path-independence. Classical systems including Michaelis-Menten kinetics, global equilibrium, and allosteric regulation are recovered as different algebraic regimes, and we develop operational tests that quantify departures from the axioms through experimentally measurable indices. The resulting framework unifies equilibrium, kinetics, regulation, and chemical computation within a single algebraic language, offering new principles for the analysis and design of responsive or self-regulating materials.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2511.16697>)

[PDF](<https://arxiv.org/pdf/2511.16697.pdf>)