Landauer Efficiency of Self-Modeling: An Operational Scale of Vitality

Complexity is ubiquitous, life is rare: stars, hurricanes, crystals, and language models are far from equilibrium, yet none closes a self-payment loop in which the model and the dissipation maintaining it belong to one physical boundary. A closed loop of self-payment separates the vital from the merely complex; we make it quantitative. We define vitality as the Landauer efficiency of self-modeling: the dimensionless ratio of the predictive information a system holds about its environment to the Landauer budget of its dissipation. Its upper bound is a conditional consequence of Landauer's principle under the stationary-accounting postulate. The decisive condition is self-payment: numerator and denominator belong to one physical system. Unlike assembly theory, integrated information, teleodynamics, and the free energy principle, the scale requires the model and its paying dissipation to share one boundary. A two-stage procedure - structural screening, then vital verification - is applied to six paradigm cases from a star to a metropolis, with E. coli chemotaxis computed in full. Structural potential is nearly universal; closed self-payment loops are rare. Three operational consequences follow: extraterrestrial-life searches must detect such loops beyond chemical biosignatures; the ethical status of an artificial system becomes whether it has begun to pay for its own model; and the boundary between the structurally complex and the vital is the positivity of the efficiency, a necessary condition. The theory addresses the stationary regime; a companion work treats the non-stationary case. The programme is open to refutation along eight independent lines, including a power-law dependence of adaptation rate on this efficiency.