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

We introduce a unified non-equilibrium thermodynamic framework to quantify the macro
scale structural stability of the Earth system, conceptualized here as a highly coupled, multi
physics dissipative manifold Ψ⊕. Rather than analyzing localized subsystems in isolation,
we construct a global, dimensionless effective state variable, denoted as the Earth System
Stability Variable L ∈ [0,1). Analogous to macroscopic accounting identities, L aggre
gates 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 formulate
the governing dynamics through a data-driven non-linear accounting functional subject to
Lipschitz continuity. We propose that near critical transitions, the high-dimensional dy
namics of the Earth system effectively project onto this single low-dimensional macroscopic
state variable. The scientific value of this framework will be determined by its measurable
predictive skill, not by the elegance of its formulation. We conclude by providing a rigor
ous three-phase implementation roadmap designed to test the framework’s predictive power
against long-term remote-sensing networks.