Ultradian Symmetry Dynamics: A Time-Resolved, Non-Equilibrium Mathematical Framework for Modeling Biological Aging

Background: Biological aging is conventionally modeled as a slow, monotonic process operating on circadian (approximately 24-hour) or multi-year timescales. This treatment neglects a well-documented layer of physiological organization at the ultradian scale, comprising oscillations with periods between roughly twenty minutes and several hours, which arise from pulsatile hormone secretion, autonomic nervous system cycling, and sub-daily metabolic rhythms. A model that resolves aging dynamics at this finer temporal grain has not, to the knowledge of the author, been formulated in closed mathematical form. Objective: This paper develops and analyzes the Ultradian Symmetry Dynamics (USD) model, a non-equilibrium, time-resolved mathematical framework in which physiological aging is represented as the evolution of a multivariate biological state vector under coupled circadian and ultradian oscillatory forcing, entropy-producing stochastic dynamics, and a symmetry-polarity structure relating conjugate physiological variables. The objective is to specify the model's axioms, derive its governing equations, define quantitative observables (spectral peak power, phase coherence, entropy production rate, phase variability), and evaluate the model's internal consistency and predictive structure using controlled numerical simulation. Methods: The USD model is built from eight postulates concerning time-scale discreteness, coupled rhythmicity, non-equilibrium thermodynamic driving, symmetry-polarity correspondence, state singularities, vibrational coherence, information polarity, and dynamic duality. These postulates are translated into a stochastic differential equation governing an n-dimensional state vector, a composite ultradian-circadian signal model with a characteristic ultradian period near 48 minutes, an information-theoretic coherence functional, and an entropy production functional derived from the Onsager formalism. The model is discretized, sampled at 10-minute resolution over a simulated 7-day observation window, and analyzed using Fourier spectral estimation, Morlet wavelet time-frequency decomposition, and circular statistics of phase distributions. Two simulated cohorts, structurally analogous to a younger and an older physiological state, are generated by parameter perturbation consistent with the model's hypotheses, and compared using standard inferential statistics. Results: Simulated time series reproduce a dominant ultradian spectral peak near 48 minutes alongside the circadian peak near 1440 minutes, consistent with the model's construction. In the simulated older cohort, ultradian peak power and mean phase coherence are reduced relative to the younger cohort, while entropy production rate and phase variability are increased, in the direction predicted by the model's hypotheses. Coherence and entropy production are strongly and inversely correlated across simulated subjects. Total propagated parameter and estimation uncertainty remains below a few percent under the sampling and spectral estimation procedures used. Conclusion: The USD model provides an internally consistent, falsifiable, closed-form framework linking ultradian oscillatory structure, information coherence, and non-equilibrium entropy production to aging-related physiological decline. Because the reported results are generated from simulation of the model's own equations rather than from empirical human physiological data, the paper is presented, and should be read, as a theoretical and computational framework paper that establishes testable, quantitative predictions for future empirical validation using real ultradian physiological time series such as heart-rate variability, core body temperature, and pulsatile hormone concentration data.