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Hamilton-Jacobi theory of quantized biological function

Francisco Monroy*

  • *Contact author: monroy@ucm.es
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APS Open Sci. 1, 000140 – Published 17 September, 2026

DOI: https://doi.org/10.1103/x2fd-pjlb

Abstract

Living systems display organized, context-dependent dynamics through a restricted repertoire of persistent functional states. At mesoscopic scales, where biological motion is classical, dissipative, and noisy, such discreteness cannot be attributed to microscopic quantum effects alone. Here, we formulate a mesoscopic theory of functional closure for thermodynamically open episodes in which regulatory organization confines the dynamics to an approximately invariant informational class. Within a constrained open Hamilton-Jacobi framework, exact dissipative composability requires the complete irreversible realization of a biological act—including bulk, interfacial, regulatory, composite, and unresolved internal contributions—to admit an exhaustive, nonredundant thermodynamic partition. In an approximately isothermal regime, causal accumulation of the total irreversible power defines a unique positive dissipative-action scale, ℏB. This act-dependent scale sets the resolution of distinguishable functional realizations, while closure defines the domain on which a global additive action invariant can be constructed. If the nontrivial closure spectrum has a least positive action scale, its admissible values form an exact lattice. Quantization in biological dissipative-action units occurs only when this primitive closure scale saturates the independently constructed thermodynamic resolution, so that the spectrum is resolved in integer multiples of ℏB. Coherent functional modes are the closure-compatible, persistent, and action-resolved realizations of these discrete classes. The theory predicts clustering of completed trajectories in actionlike observables and separates state correlation, hidden dissipation, and information-geometric distinguishability from the exact composability of irreversible physical cost.

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APS Open Sci. 1, 000140– Published 17 September, 2026
Vol. 1
  • Received 24 June 2026
  • Revised 9 August 2026
  • Accepted 20 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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