Dynamics on the CES Potential Landscape: Fluctuation Theorems, Conservation Laws, Business Cycles, and Endogenous Complementarity

The companion papers establish that the CES potential Φ_q = Φ_CES(ρ) − T·S_q with q = ρ governs equilibrium selection in economies with CES production technology (curvature K) and information frictions (T = 1/κ), and that the curvature parameter K = (1−ρ)(J−1)/J simultaneously controls superadditivity, correlation robustness, strategic independence, and network scaling. This paper develops the full dynamical theory on that CES potential landscape. Four families of results emerge. Part I (Dynamical Consequences) treats the CES potential as a landscape on which the economy evolves: adjustment dynamics derive the multi-level timescale hierarchy from the Hessian eigenstructure; the Variance-Response Identity operationalizes information friction as the ratio of productivity variance to shock responsiveness; pre-crisis deceleration near regime boundaries generates ordered early warning signals; the Symmetric Adjustment Theorem constrains cross-sector coupling; noise-driven transition rates convert deterministic crossing predictions into probability distributions; the Minimum Policy Cost Theorem bounds policy costs from below; and multi-scale aggregation identifies ρ and T as the only parameters surviving aggregation. Part II (Conservation Laws) derives exact constraints from the CES potential's symmetries. Part III (Business Cycles) derives endogenous oscillations from the conservative-dissipative structure: the ρ-ordering theorem predicts sectors enter recession in order of complementarity. Part IV (Endogenous ρ) closes the framework: four channels drive ρ evolution on different timescales, producing a stable endogenous cycle reproducing the Perez technology wave.