Emergence of Active Inference from a Chemical Oscillator: A Constructive Approach to Pre-genetic Homeostasis

How could primordial life, before the evolution of genetic systems, adapt to fluctuating environments and achieve homeostasis? This study proposes a minimal, chemically plausible model where homeostasis emerges from a simple chemical reaction network. It utilizes an internal Lotka-Volterra chemical oscillator as a "search engine" to periodically vary a protocell's pigmentation. The system then optimizes its internal state by evaluating the temporal correlation between these internal fluctuations and a single global metric,the cell's self-replication rate, through a 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 amidst significant environmental fluctuations. These findings provide a constructive proof-of-concept for how a core process of active inference can emerge from a simple physicochemical system, offering a concrete scenario for the acquisition of adaptive capabilities at the origin of life.