How greedy is the Universe? An entropy ledger and a causal envelope for early black hole growth

Abstract

The entropy of the observable Universe is dominated, by fifteen orders of magnitude, by the horizons of supermassive black holes, and gravitational collapse into black holes has often been proposed as the Universe's preferred channel of entropy production. We examine this suggestion quantitatively, and the analysis largely refutes it. Three results are presented. First, an entropy production history: the rate $dS/dt(z)$ resolved by channel, from the star formation history and a Soltan-normalized accretion history. Black hole horizon growth exceeds all radiative channels by a factor $\sim 10^{16-17}$ after the first seeds; the total rate peaked near $z\approx 1$--$2$ and has since declined; the late peak is structural, because horizon entropy production weights accretion by the accretor's mass and the most massive accretors are assembled last. Second, a causal-hydrodynamic envelope: the fastest entropy-producing trajectory permitted by causality and gas dynamics, $\dot M \sim c_s^3/G$ in atomic-cooling halos, which reaches $10^{7\pm1}\,M_\odot$ by $z\approx 8$--$10$ without radiative throttling, and whose phenomenology (obscured, radiatively inefficient, X-ray weak, red) closely resembles the JWST little red dots. The realized-to-envelope ratio defines an efficiency $F(z)$, which remains between $10^{-7}$ and $10^{-4}$ throughout $4\le z\le 12$, even under the most generous JWST-era bracket. Third, order-of-magnitude no-go results: Boltzmann weighting of collapse channels by entropy gain, dissipative adaptation applied to self-gravitating systems, and any strong maximum-entropy-production principle in cosmology all fail at leading order, by factors of up to $10^{16}$. The Universe produces entropy overwhelmingly through black holes, yet remains far below its own envelope at all times. Whatever selects cosmic structure, it does not maximize entropy production.