arXiv subjects

Srinivasa Rao Thirunagari

Publications and source records attributed to Srinivasa Rao Thirunagari.

2 recordsLinked to original sources

arXiv2026

Operational Regimes of Ternary $Γ$-Semiring Chemical Systems

Ternary $Γ$-semiring chemical systems provide an algebraic language in which mediators such as catalysts, solvents, inhibitors, thermodynamic conditions, and external fields enter the transformation law as internal arguments. Building on the published MATCH foundation article, this paper studies operational regimes of the compressed TGS notation rather than proposing a second axiomatization. Distributivity is interpreted as observable non-interference of mediated channels, while associativity is interpreted as observable path-independence of bracketed mediated protocols. Since the state space is only semigroup- or semiring-level, subtraction is not used at the state level; instead, observable defect and ratio indices are defined after applying a non-negative observable. We prove that distributivity implies observable non-interference under observable additivity, and that associativity implies observable path-independence. Nonzero defects detect observable distinguishability. To strengthen the diagnostic layer, we prove recovery theorems showing that separating families of observables can recover algebraic distributivity and associativity from vanishing observable defects. We also introduce approximate operational regimes and prove ratio bounds controlled by uniform defect estimates. Under strict convexity, uniqueness, and common global-constraint assumptions, a potential-generated equilibrium operation is shown to be associative. A symbolic intermediate-dependent Michaelis--Menten type construction shows how non-associativity may arise in kinetic regimes, and regulatory/allosteric-type non-distributivity is discussed cautiously through observable coupling.

physics.chem-ph↗

arXiv2026

Axiomatic Foundations of Chemical Systems as Ternary $Γ$-Semirings

Chemical transformations depend not only on the identities of the reacting species but also on the catalytic, environmental, and intermediate conditions under which they occur. Classical binary reaction formalisms usually treat such conditions as external annotations, which obscures the genuinely multi-state and multi-parameter character of real chemical processes. In this paper we introduce an axiomatic framework in which a chemical system is modelled by a ternary $Γ$-semiring. The elements of the state set represent chemical states, while the parameter set encodes catalytic and environmental conditions. A $Γ$-dependent ternary operation is used to describe mediated transformations, treating reactants, intermediates, and mediators as intrinsic arguments of the transformation law. We develop the algebraic axioms governing these mediated interactions and interpret their associativity, distributivity, and $Γ$-linearity in terms of multi-step pathways, parallel processes, and controlled environmental dependence. We introduce chemical ideals and $Γ$-ideals as algebraic structures modelling reaction-closed sub-systems and pathway-stable domains, and study their prime and semiprime forms. Homomorphisms between TGS-chemical systems are shown to preserve reaction pathways and describe consistent changes of chemical environment. Abstract examples from catalysis, thermodynamic phase control, and field-induced quantum transitions illustrate how familiar chemical phenomena fit within this framework. The resulting theory provides a unified algebraic foundation for multi-parameter chemical behaviour and establishes the structural basis for subsequent developments involving kinetics, geometric methods, and computational or AI-assisted models.

math.RA↗