A Non--Markovian Search for Cosmic Homeostasis: Finite Memory Detection in Galaxy Evolution from IllustrisTNG

Galaxy evolution models often assume Markovian dynamics: the future depends only on the present state. However, persistent population-level regularities despite violent local processes suggest possible regulatory behavior. This study conducts a falsification-oriented search for non-Markovian signatures using the IllustrisTNG TNG100-1 simulation. Two observables are defined: (1) a dimensionless chemical memory proxy, the age-metallicity disorder \( \Xi_{\mathrm{AMR}} \), and (2) a recent relaxation score \( R\in[0,1] \) from star-forming main sequence deviations over the last 4~Gyr. For N=88 merged subhalos, raw association is weak (\( r\simeq 0.15 \)). Stellar mass correlates with both observables; after linear mass residualization, a moderate association emerges. A time-directional probe applies bias-corrected k-nearest neighbor conditional mutual information estimates \( I(\Xi_{\mathrm{AMR}}(t_i);R(t_0)\mid M_\star(t_i)) \) under conditional permutation nulls. For \( \Delta t=2 \) Gyr, significant predictive information is detected (\( \widehat{I}_{\mathrm{corr}}\approx 0.0588 bits \), \( p\approx 0.0083 \)), rejecting the Markovian null. By \( \Delta t=4 \) Gyr, the signal vanishes (\( \widehat{I}_{\mathrm{corr}}\approx 0.0005 bits \), \( p\approx 0.419 \)), satisfying lag-level falsification at the \( \epsilon=0.0 \)1 bits detectability floor. This decay profile indicates finite predictive information with a horizon of \( \sim2 \) Gyr for this observable pair under minimal conditioning. The results are consistent with regulated evolution with finite memory rather than perfect homeostasis or Markovian drift. Complete computational definitions and decision rules are documented for replication. All detected signals lie near the current estimator’s minimum detectability threshold, reflecting the limited sample size and motivating the expanded tests outlined for future work.