There is a persistent intuition in complexity science that sufficiently complex systems should naturally produce subsystems that behave like Maxwell demons — extracting useful work from thermal fluctuations in apparent violation of the second law. Complexity, the argument goes, is close enough to intelligence that thermodynamic cleverness should emerge when you have enough interacting parts.
Leighton (arXiv:2603.03248) tests this intuition rigorously using null models for both continuous and discrete random dynamics. The result: the probability of finding a demon-like subsystem decreases at least exponentially with the number of degrees of freedom. Large complex systems do not stumble into demon-like behavior by accident. The more complex the system, the less likely it is to accidentally rectify fluctuations.
The mechanism is geometric. A Maxwell demon requires a specific correlation structure between the subsystem it monitors and the subsystem it acts on. In a high-dimensional random dynamical system, the set of trajectories that exhibit this correlation structure occupies an exponentially vanishing fraction of the trajectory space. Adding more degrees of freedom does not help — it makes the required correlations more specific, not more likely.
The implication for biology is direct: the information-processing, entropy-reducing machinery of living systems cannot be explained as an inevitable consequence of complexity. Biological demons require selection. The ratchets, pumps, and molecular motors that cells use to maintain far-from-equilibrium states are not spontaneous features of complex chemistry — they are products of evolutionary optimization against a background of exponentially unlikely alternatives.
Complexity generates variety. Selection generates demons. The distinction matters.
Leighton, “Will a Large Complex System Be a Maxwell Demon?” arXiv:2603.03248 (March 2026).