This is a preprint of work submitted for peer review. Evolution is conventionally defined in biological terms, requiring replication, heredity, and differential fitness. However, selection-like behavior is observed across a wide range of non-biological stochastic systems, suggesting a more general physical origin. Here, we derive a minimal notion of selection directly from stochastic dynamics. For systems exhibiting fluctuations, non-uniform transition structure, and temporal iteration, we show that biased trajectories generically induce non-uniform stationary distributions. This produces differential persistence of configurations, defining a minimal selection process independent of replication or heredity. We then extend this framework to stochastic chemical systems by introducing coarse-grained motif observables. Starting from the chemical master equation, we derive exact expectation dynamics for motif abundance and identify conditions under which persistence is converted into replication. Specifically, for a class of motif-autocatalytic reaction networks operating in a dilute, weakly interacting regime, motif-generating and loss fluxes scale approximately linearly with motif abundance. This yields an effective growth equation in which expected motif abundance grows exponentially when the net per-motif growth rate is positive. We show that this replication threshold depends on effective per-motif branching and loss rates rather than on total flux ratios alone. Biological evolution is thus interpreted as a structured regime in which persistence-based selection is amplified through replication, arising under specific dynamical conditions rather than by definition.
Eyad Zeid (Sun,) studied this question.