Recurrence Without a Motor: Minimal Structural Conditions for Recurrence and Drift

Why do systems repeatedly re-encounter themselves rather than dissipate into irrelevance?Across disciplines, recurrence is often explained by invoking an implicit motor: rotation, cyclic forcing, oscillation, or a privileged dynamical cause. This paper rejects that framing. It argues that recurrence requires no driver. Instead, recurrence arises as a structural default whenever minimal conditions are satisfied. The paper establishes three such conditions: partial conservation, output-to-input coupling, and effective boundedness. When a system cannot fully dissipate, cannot fully decouple its outputs from future inputs, and cannot expand without bound, repeated self-encounter is not an added hypothesis but the expected organization of process. Recurrence is treated not as a cause, force, or ontological principle, but as a structural consequence of constraint. A second upstream condition is then isolated: nonlinearity. While recurrence alone may be structurally neutral in idealized regimes, the presence of nonlinearity renders neutrality non-generic. Under recurrence, nonlinearity converts asymmetries, constraint couplings, thresholds, and saturation effects into cumulative structural consequences. As a result, repeated recurrence becomes a source of structural drift—not in a semantic or teleological sense, but as a change in the admissible structure of system behavior. The paper formulates these claims in a domain-agnostic manner and specifies explicit failure conditions under which recurrence or drift becomes negligible: full dissipation, strict feedforward organization, unbounded escape, global linearity, perfect cancellation, or complete independence of constraints. These conditions provide local falsifiability rather than metaphysical generalization. Finally, the paper clarifies the exact bridge to the law-level operator Ψ = ∂S/∂R. Once recurrence is structurally unavoidable and nonlinearity makes structural drift non-accidental, the question of measuring structural change per unit recurrence becomes coherent. This paper remains deliberately pre-law: it neither introduces nor justifies the law hypothesis, but establishes why recurrence should be expected and why recurrence cannot be assumed to be structurally inert. --- Intellectual Property & ContactKOGNETIK® is a registered trademark of Serkan Elbasan (Germany).The KOGNETIK Research Series is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0). All scientific works within the series are open for citation and derivative research under proper attribution.For partnerships, translations, or applied development inquiries:✉️ research@kognetik.de · 🌐 https://www.kognetik.de --- Kognetik Series Information KOGNETIK — Minimal Operator Definition of Reflexivity (Ψ = ∂S/∂R) Reflexivity as structural rate-of-change:Ψ=∂S/∂R measures structural drift under recurrence. Process, not state:Reflexivity is a transformation rule, not a content or level. Domain-independent operator:Valid across biological, cognitive, artificial, social, industrial, and geophysical systems. Non-ascriptive, empirically testable:Ψ compares systems by observable structure and recurrence. Higher-order phenomena as specifications:Learning, adaptation, consciousness, governance, and identity are structured regimes of Ψ.