Life Ratio: A Minimal Theoretical Framework for Biological Persistence from Non-Equilibrium Thermodynamics, Information Theory, and Dynamical Systems

Abstract A general theory of biological persistence requires a formalism that is sufficiently minimal to apply across scales, while remaining compatible with first principles in physics. Contemporary biological descriptions often privilege one domain—metabolism, information, complexity, or damage accumulation—without embedding these within a single coherent mathematical architecture. This paper proposes Life Ratio as a conceptual framework in which biological viability is represented as the balance between available energy, functional information, and internal chaos. Λ(t) = [Ē(t)^α × Ī(t)^β] / [Ċ(t)^γ], α, β, γ > 0 Here, Ē, Ī, and Ċ are dimensionless normalised forms of available energy, functional information, and internal chaos, respectively. The framework is not presented as an empirically validated biomarker or clinical score. Rather, it is derived as a minimal admissible functional form under a set of viability axioms: non-equilibrium persistence requires free-energy throughput, function-preserving organisation requires physically instantiated information, and continued viability requires bounded internal disorder. Using arguments from non-equilibrium thermodynamics, statistical mechanics, information theory, and hazard-based formulations of persistence, it is shown that any viability measure satisfying the relevant monotonicity, boundary, and scale-consistency conditions belongs naturally to a multiplicative numerator/divisive denominator class. The framework is then interpreted in relation to development, ageing, disease, and evolutionary persistence. Life Ratio is therefore advanced as a canonical conceptual scaffold for theoretical biology and related quantitative disciplines.