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

Fernando Izaurieta, Cristian Quinzacara, Omar Valdivia

First listed 2026-08-04 | Last updated 2026-07-31

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.

Short digest

This paper builds a cosmic entropy-production ledger from the star-formation history and a Soltan-normalized black-hole accretion history, finding that supermassive-black-hole horizon growth has exceeded radiative channels by roughly 10^16–10^17 since the first seeds and peaked structurally at z≈1–2. It then defines a causal-hydrodynamic upper envelope for early growth in atomic-cooling halos, where unthrottled inflow at \dot{M}∼c_s^3/G can reach 10^(7±1) M⊙ by z≈8–10 and yields an obscured, X-ray-weak, red phenomenology consistent with JWST little red dots. Yet the realized entropy-production rate remains only 10^-7–10^-4 of this envelope over 4≤z≤12, leading the authors to argue that neither black-hole assembly nor cosmic structure formation behaves as a strong maximum-entropy-production process.

Key figures to inspect

• Figure 1. This is the core entropy ledger: it shows that black-hole horizon growth overwhelms stellar and other radiative entropy channels by 16–17 orders of magnitude, while also placing the observed history beneath the causal-hydrodynamic envelope and showing the LRD-enhanced accretion bracket.
• Figure 2. This figure makes the early-growth argument concrete by comparing the causal-hydrodynamic envelope with Eddington-limited seed tracks and with J0313-1806, GN-z11, CEERS 1019, UHZ1, and the revisable little-red-dot mass range. It is the clearest visual link between the proposed extremal trajectory and the JWST-era black-hole population.
• Figure 3. This conclusion-driving diagnostic plots the realized-to-envelope entropy efficiency for both the Soltan-normalized and LRD-bracket histories. Its central result is that the Universe stays four to seven orders of magnitude below the maximum allowed greed at every relevant epoch.