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

Many biological processes involve coordination across distributed oscillatory or rhythmic assemblies. This model asks whether a specified phase-alignment criterion can reproduce tens-of-milliseconds registration times, and how its waiting time changes with modular depth.

We model biological temporal processing as a sequence of state registrations: operationally defined events at which a distributed system stabilizes or exposes an output. A registration can involve irreversible memory formation or reset, but it is not thermodynamically irreversible by definition. The paper compares four candidate timescales:

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

For its cortical visual-processing parameterization, the paper places quantum speed limits at $\sim 10^{-13}$ s, power estimates at $10^{-15}$–$10^{-8}$ s, signal detection at $\sim 10^{-3}$ s, and coherence time at $\sim 10^{-2}$ s. This is a regime-specific comparison, not a universal Landauer timing law; within the stated model, coordination is the slowest term.

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.

Transient phase-delta dynamics do not incur a Landauer cost merely because they evolve continuously, just as digital dynamics do not incur it on every clock. Landauer's bound becomes relevant when an implemented protocol logically erases alternatives, such as resetting a stabilized memory. Coupling, maintenance, noise suppression, and control can consume energy throughout the pre-commit interval; those costs must be calculated from the actual device rather than described as "below Landauer."

The framework identifies extracellular electric fields as one candidate contributor to pre-commit coordination. Neural tissue also contains continuous, spatially extended chemical, electrical, and mechanical variables, so uniqueness is not established. Evidence that ephaptic fields can modulate spike timing makes a causal role plausible in some preparations, but it does not establish the effect size or computational role in intact circuits. Those require direct perturbation, matched controls, and comparison with synaptic and other field-mediated explanations.

Kuramoto simulations reproduce the proposed scaling within selected toy network architectures; they test the internal model, not its biological validity:

• 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 may modulate registration opportunities and thereby contribute to $\lambda_{\mathrm{attempt}}$. Interpreting a perception set as a larger coordination depth $M$ is a modelling proposal. Whether measured coordination depth predicts prospective timing, retrospective duration, or neither is an empirical question.

Tachypsychia: A dual-loop account is an exploratory hypothesis: a high-$M$ perceptual loop could dissociate from a faster motor loop under acute stress. The model does not yet establish that this mechanism causes subjective-time dilation.

The paper proposes a two-parameter exploratory description using measured effective dimension ($D_{\mathrm{eff}}$) and a defined registration rate ($\Gamma_{\mathrm{commit}}$). Drug classes may alter either quantity, but neither is a consciousness score or a physical clock.

• Psychedelics: test whether task- and scale-specific changes in $D_{\mathrm{eff}}$ covary with prospective timing and retrospective duration, which should be analysed separately.
• Deliriants: test whether increased neural noise can be distinguished from structured changes in effective dimension and from failures of memory or report.
• Anaesthetics: test changes in $D_{\mathrm{eff}}$, connectivity, perturbational response, and report together; no subjective duration can be inferred when experience or recall is unavailable.
• Stimulants: test whether changes in temporal resolution occur without the same effective-dimension signature.

These are losable hypotheses requiring preregistered measurements, competing predictors, and explicit observation scales. The framework does not predict one monotonic dimension-to-time or dimension-to-consciousness law.

Coherence time—the waiting time for distributed oscillatory assemblies to achieve a stated alignment criterion before operational registration—scales exponentially with coordination depth $M$ in the modular regime. Under the paper's neural parameterization, multi-module coordination is slower than the alternative floors considered. Landauer's principle does not itself supply a registration-time bound without a physical reset, error target, and protocol.

The central model result is a speed-flexibility trade-off: increasing $M$ exponentially slows criterion crossings in the modular approximation while expanding the represented combination space, and increasing coupling $r$ speeds crossings while compressing the simulated dynamics. The expected scaling is reproduced in the paper's modular Kuramoto simulations; it is not yet a general empirical law. The framework matches binding-window order of magnitude under its selected neural 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.