Variance-dependent inheritance fidelity drives residence-time symmetry breaking in a protocell model

Symmetry breaking in prebiotic and protocellular systems is often attributed to fitness gradients, catalytic amplification, or explicit selective advantages. The present study tests whether direction-neutral, state-dependent variance coupling can generate residence-time asymmetry in finite protocell populations without mean-fitness bias or explicit directional preference. Two paired-noise stochastic models are analyzed. Model A implements a Moran birth-death process in which reproduction probability depends on a symmetric internal-variance proxy. Model B combines threshold-triggered division with composition-dependent partition noise, such that inheritance fidelity varies symmetrically with internal composition. In both models, the update rules preserve exchange symmetry under p→1-p, although state-dependent variance coupling can alter local persistence across state space. Asymmetry is quantified using a pre-registered neutral-quantile threshold, defined as the 0.99 quantile of the neutral symmetry-distance distribution after burn-in, thereby fixing the expected false-positive rate at 1%. Model A produced only weak and parameter-sensitive increases in time spent away from symmetry. In contrast, Model B produced strong persistence away from symmetry in the high-coupling regime. Neutral-equivalence sanity checks confirmed exact matching at zero coupling, validating the paired-noise implementation. These results are consistent with the idea that variance-dependent inheritance fidelity provides a biologically relevant protocell realization of multiplicative-noise- driven ordering in nonequilibrium populations.