Two views of the brain are reconciled by a unifying principle of maximal information processing.

There is selective pressure on brains to maximize computational capacity and adaptability in an unpredictable world. Prior work suggests that this demand is satisfied by a regime called criticality, which has emerged as a powerful, unifying framework for understanding how computation can arise in biological systems. However, this framework has been confined to high-dimensional network models. At first glance, this appears irreconcilable with many of the foundational, low dimensional dynamical models that have driven progress in theoretical and computational neuroscience for a century. If criticality is a universal principle, then all models that accurately capture significant aspects of brain function should be constrained by the same fact. Lacking a definition of criticality in low-dimensional dynamical systems, this has been impossible to evaluate. Here, we develop a mathematical definition of criticality that transcends dimensionality by recognizing temporal scale invariance as analogous to spatial scale invariance that defines criticality in large systems. We demonstrate that there are two mechanistically distinct sources of criticality at bifurcations, one deterministic and one that emerges from noise fluctuations. Further, we show that some but not all canonical bifurcations in neural models exhibit criticality, and only a subset of these are biologically plausible. We conduct numerical analyses demonstrating that information processing capacity peaks at critical bifurcations, and evaluate which historically influential neural models contain these bifurcations. Our results establish criticality as a universal neurobiological principle that is accessible to systems of any dimensionality. This unifies disparate modeling approaches under a single computational framework and suggests that optimal information processing emerges not from model-specific mechanisms but from fundamental properties of critical dynamics themselves.