When Combinatorial Complexity Meets Equilibrium: Macroscopic Fluctuations and Zipf’s Law
In conventional thermodynamic systems, fluctuations are expected to vanish as V⁻¹ᐟ², reflecting the effective independence of spatially separated degrees of freedom. This intuition can fail in a chemical space that grows combinatorially. We show that, even at equilibrium, a reaction network of molecular assemblies develops a statistically relevant sector of rare species with persistent finite-size fluctuations. The same combinatorial structure generates a Zipf-like rank-frequency distribution. Rather than requiring preferential growth, optimization, or an explicit selective mechanism, here the apparent selection among species follows directly from equilibrium dynamics acting on an exponentially expanding space of possible structures.
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