Biological function as quantized organised action.

Biological systems often realise function through restricted repertoires of persistent states and reproducible trajectories, despite operating far from equilibrium under noise and dissipation. This paper develops a mesoscopic theory for such discreteness in functionally closed biological systems. A functional act is a thermodynamically open episode over an operational time window τB=t2-t1, during which all participating domains remain engaged in the same regulated process. The internal entropy-production rate σ(t) quantifies irreversibility, so that T0σ(t)≥0 is the dissipative power in an approximately isothermal regime, composable over an admissible non-overlapping partition of operationally simultaneous domains. The resulting act-level dissipative action, ħB≡AΣ(σ;τB), is not a microscopic quantum or universal constant, but an act-dependent resolution scale for distinguishable functional realisations. Functional closure supplies an induced action invariant, J¯. If its additive spectrum has a least positive element J∗, then it is the exact lattice J∗Z; under saturation, J∗=ħB, the physically realised non-trivial sector satisfies J¯=nħB, with n∈Z+. The resulting functional states are closure-compatible, dissipatively resolved realisations of organised biological action. The theory predicts action-space clustering and distinguishes sub-resolution continuity from breakdown caused by loss of closure, persistence or operational simultaneity.