Eigenvalues, Entropy, and Why Systems Stay Stable or Collapse
In complex dynamic systems, stability emerges from the delicate interplay of mathematical eigenvalues and thermodynamic entropy. Eigenvalues act as multipliers that shape how systems evolve, determining whether growth accelerates or decays. Entropy, a measure of disorder, quantifies the predictability of system states, revealing how randomness drives divergence from order. Together, they define whether a system converges to stability or fragments into chaos. The Role of Large Systems and Statistical Resolvability For meaningful predictions, systems must approximate statistical stability—this demands large sample sizes, often around n ≈ 30, enabled by the…
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