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 = \int \boldsymbol{\tau} \cdot d\boldsymbol{\theta}) is balanced by Lindblad dissipation \mathcal{D}[\rho] and Landauer entropy production (S = -\operatorname{Tr}(\rho \ln \rho)) into the mantle thermal reservoir under the Symmetry–Entropy Duality \delta(S_{\text{sym}} + S_{\text{ent}}) = 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 \tau_E = 433.2\text{ days} and \tau_M = 206.9\text{ days}; 3. The Amplitude Disparity is Quantified: Mars's ninety-fold amplitude suppression (\sim 10\text{ cm} vs. \sim 9.0\text{ m}) follows from the geometric axisymmetry of polar \text{CO}_2 deposition, the extinction of its core homopolar dynamo (\boldsymbol{\tau}_{\text{EM}} \to 0), and the quenching of the innovation core (2^1 - 2 = 0).