Coherence Time in Biological Oscillator Assemblies Bounds the Rate of State Registration

Biological computation—from neural binding to cardiac pacemaking to circadian coordination—depends on coherent oscillations across distributed assemblies. Why does visual binding require 30–50 ms rather than 3 ms or 300 ms? Why do larger assemblies integrating more information process more slowly?

We model biological temporal processing as a sequence of state registrations—thermodynamically irreversible events that commit high-dimensional internal state as low-dimensional output. The minimum time between registrations is bounded by four physical constraints:

$\tau_{\mathrm{eff}} = \max\left[\tau_{\mathrm{QSL}},\; \tau_{\mathrm{SNR}},\; \tau_{\mathrm{coh}},\; \tau_{\mathrm{power}}\right]$

The hierarchy for cortical visual processing places quantum speed limits at $\sim 10^{-13}$ s, power limits at $10^{-15}$–$10^{-8}$ s, signal detection at $\sim 10^{-3}$ s, and coherence time at $\sim 10^{-2}$ s. The bottleneck is not energy or quantum mechanics—it is coordination.

Between commits, the system occupies a phase delta regime: structured inter-module phase relationships that bias downstream outcomes without yet registering a discrete state. This interval is computationally productive—analog computation occurring before the commit readout.

Because phase-delta dynamics are pre-committal and reversible, they need not incur the per-bit Landauer cost associated with irreversible erasure. The relevant energy cost is the coupling energy required to sustain structured bias, not a per-bit erasure cost. This places the phase delta regime below the Landauer threshold—a sub-Landauer mode of computation.

The framework identifies the extracellular electric field as a candidate substrate for pre-commit coordination: it is the only substrate in neural tissue that is simultaneously continuous, spatially extended, and high-dimensional. Ephaptic coupling modulates spike timing, and timing is causally significant (the paper's central result), so the field's causal significance follows from two independently supported premises.

Kuramoto simulations validate the expected scaling across three network architectures:

• Modular coupling: strongest support, with near-independent modules and $R^2 = 0.97$, $\hat{\alpha} = 0.99$
• All-to-all coupling: regime-boundary case; very high coherence makes the theory-consistent fit ill-conditioned
• Sparse coupling: poor fit ($R^2 = 0.28$), indicating collapse of the modular-compression assumption

The framework predicts its own regime of validity: modular or hierarchical coordination structure supports the rare-event scaling argument; unstructured networks do not. Kaplan-Meier survival analysis handles censored first-passage times. Robustness checks confirm the scaling exponent is insensitive to dwell-time threshold variation, and within-module coherence does not systematically decline with module count.

Visual binding windows (27–54 ms): $M \approx 8$ occipital modules with $r \approx 0.7$–0.8, $\varepsilon \approx \pi/2$, and $\lambda_{\mathrm{attempt}} \approx 126$ s$^{-1}$ recover coherence times in the empirical binding-window range. This is an order-of-magnitude existence proof, not a precise prediction—the framework's testable content lies in its scaling predictions.

Alpha oscillations and perception sets: Alpha frequency modulates commit opportunity windows, effectively setting $\lambda_{\mathrm{attempt}}$. Recent work by Wutz (2024) shows alpha reflects internally generated "perception sets" rather than passive temporal sampling. A perception set can be interpreted as a high-dimensional internal template (large $M$), and the temporal effects—dilation under richer processing, compression under impoverished conditions—correspond to the exponential dependence of $\tau_{\mathrm{coh}}$ on coordination depth.

Tachypsychia: A dual-loop hypothesis explains why acute stress dilates subjective time without improving temporal resolution—a slow, high-$M$ perceptual loop dissociates from a fast, low-$M$ motor loop.

The framework predicts qualitatively different temporal phenomenology across drug classes from a two-parameter structure ($D_{\mathrm{eff}}$, $\Gamma_{\mathrm{commit}}$):

• Psychedelics (psilocybin, DMT, LSD): increase $D_{\mathrm{eff}}$ and decrease $\Gamma_{\mathrm{commit}}$, predicting time dilation with experiential richness
• Deliriants (scopolamine, diphenhydramine): increase neural noise without structured $D_{\mathrm{eff}}$ increase, predicting time confusion without time dilation—the framework's most discriminating pharmacological prediction
• Anaesthetics (propofol, sevoflurane): decrease $D_{\mathrm{eff}}$, predicting time compression toward unconsciousness
• Stimulants (amphetamine, caffeine): increase $\Gamma_{\mathrm{commit}}$ without substantially altering $D_{\mathrm{eff}}$, predicting mild time expansion with increased temporal resolution

The key empirical test: subjective time dilation should correlate with the participation ratio of neural dynamics ($D_{\mathrm{eff}}$), not with broadband spectral entropy.

Coherence time—the time required for distributed oscillatory assemblies to achieve sufficient phase alignment for irreversible state registration—scales exponentially with coordination depth $M$ in the modular regime. The unified bound shows that in biological neural systems, quantum speed limits and Landauer bounds are not rate-limiting; multi-module coordination provides the binding constraint, exceeding quantum floors by approximately eleven orders of magnitude.

The central validated finding is the speed-flexibility trade-off: increasing $M$ exponentially slows commits but expands combinatorial flexibility, while increasing coupling $r$ speeds commits but restricts dynamics to low-dimensional manifolds. The framework recovers binding-window timescales from independently constrained parameters and yields concrete tests of entrainment linearity, modularity dependence, and temporal-resolution scaling with coordination depth.

More exploratory extensions—phase-delta dynamics, candidate biophysical substrates, and subjective-time predictions based on $D_{\mathrm{eff}}/\Gamma_{\mathrm{commit}}$—remain hypotheses that are now explicitly linked to measurable quantities. The primary limitation is the requirement for identifiable modular structure.