An Open-System Operator Architecture for the Chandler Wobble on Earth and Mars

By synthesizing open-system statistical mechanics, non-linear attractor dynamics, and an operator-theoretic formulation, this paper unifies the comparative rotational nutation of Earth and Mars: 1. The Classical Dilemmas are Resolved: The Chandler wobble is established as an open, non-equilibrium dissipative limit-cycle attractor. Continuous geophysical work (W = ∫ τ · dθ) is balanced by Lindblad dissipation D[ρ] and Landauer entropy production (S = -Tr(ρ ln ρ)) into the mantle thermal reservoir under the Symmetry–Entropy Duality δ(Ssym + Sₑₙₜ) = 0; 2. The Period Ratio is Derived from First Principles: Grounded in the Ehrenfest non-rigidity mandate, mantle elastodynamic Love numbers (k_2 / k_s) yield periods of τ_E = 433.2 days and τ_M = 206.9 days; 3. The Amplitude Disparity is Quantified: Mars's ninety-fold amplitude suppression (~ 10 cm vs. ~ 9.0 m) follows from the geometric axisymmetry of polar CO_2 deposition, the extinction of its core homopolar dynamo (τEM → 0), and the quenching of the innovation core (2^1 - 2 = 0).