A constructive chemical oscillator model demonstrates the emergence of homeostasis before genetic information through active inference

Homeostasis is a fundamental property of life, intricately regulated by genetic information in extant organisms. However, a central mystery in the origin of life is how primordial life, before the establishment of a genetic system, could have adapted to fluctuating environments and acquired homeostatic capabilities. To address this question, this paper proposes an abstract, proof-of-concept mathematical model to explore how homeostasis could emerge through self-organization from a simple chemical reaction network, without reliance on genetic information or externally defined setpoints. Crucially, the system does not require direct sensory information of either the target value ( T opt ) or its current state ( T cell ); it only evaluates the resulting global performance metric (replication rate). The model utilizes an internal Lotka-Volterra chemical oscillator within a protocell as a “search engine” to periodically vary the system’s phenotype (cell pigmentation). The system then adjusts its internal state by evaluating only the temporal correlation between these internal fluctuations and a single, global performance metric—the cell’s self-replication rate. This simple loop of “exploration by oscillation and optimization by correlation” is realized through a chemically implementable mechanism termed “antagonistic memory molecules.” Numerical simulations demonstrate that the model can autonomously converge to and maintain the optimal temperature for its self-replication, even amid significant fluctuations in the external environment (e.g., solar luminosity and water temperature). These results present the model as a constructive proof-of-concept, demonstrating how a core process of active inference under the free energy principle—minimizing prediction error through action—can emerge from a simple physicochemical system. This research provides a concrete scenario for the acquisition of adaptive capabilities at the origin of life and offers new guiding principles for the design of self-adaptive systems.