Emergent Information Formation in Prebiotic Protocell Clusters: A Computational Mechanics Framework of $\epsilon$-Machines and Attractor Memory

Abstract

Casimir-Lifshitz forces generate an unavoidable, long-range attraction between protocells under prebiotically realistic conditions. This interaction stabilizes mesoscale clusters such as tetrahedra, octahedra, and 13-cell icosahedra. These highly symmetric assemblies act as persistent macrostates whose transitions remain reproducible despite microscopic noise. A physics-guided coarse-graining yields a well-defined mesodynamics that can be represented as an $\epsilon$-machine: a small deterministic automaton whose causal states correspond to cluster attractors and whose transitions encode ordered reconfiguration pathways. The theory of Rosas et al. (Software in the natural world) shows that such systems can become informationally, causally, and computationally closed, thereby forming an autonomous proto-software layer. In this framework, prebiotic information does not arise from polymers but from attractor-based memory and structured transition dynamics in a purely physical cluster process.