A Dimensionless Macroscopic State Variable for Earth System Stability: An Effective Theory Approach

We introduce a unified non-equilibrium thermodynamic framework to quantify the macroscale structural stability of the Earth system, conceptualized here as a highly coupled, multiphysics dissipative manifold Ψ⊕. Rather than analyzing localized subsystems in isolation,we construct a global, dimensionless effective state variable, denoted as the Earth SystemStability Variable L ∈ [0,1). Analogous to macroscopic accounting identities, L aggregates planetary-scale residuals across five empirical domains: thermal, fluidic, chemical,informational, and structural.By mapping the planet’s Lorenz available free energy as A⊕ = A0(1 −L), we formulatethe governing dynamics through a data-driven non-linear accounting functional subject toLipschitz continuity. We propose that near critical transitions, the high-dimensional dynamics of the Earth system effectively project onto this single low-dimensional macroscopicstate variable. The scientific value of this framework will be determined by its measurablepredictive skill, not by the elegance of its formulation. We conclude by providing a rigorous three-phase implementation roadmap designed to test the framework’s predictive poweragainst long-term remote-sensing networks.