Abstract
Many open, driven systems maintain low-entropy structure far longer than microscopic relaxation times by coupling feedback control to free-energy reservoirs. We develop a chronodynamic perspective organised around two effective characteristic times: a feedback time τfb(S), describing how quickly corrective dynamics restore a structure S, and a dissipation time τdiss(S), describing how quickly open-loop processes would erase it. Their ratio defines the dimensionless persistence number Π(S) = τdiss(S) / τfb(S).
The Chronodynamic Persistence Principle (CPP) states that robust feedback-maintained persistence requires Π > 1, interpreted conservatively through a mode-wise bottleneck Πmin in multi-mode systems. We ground CPP in Freidlin–Wentzell large-deviations theory, showing that the established connection between barrier height and mean first-passage time maps precisely onto Π, yielding exponential lifetime scaling for Π > 1 and a diffusion-limited floor for Π < 1.
Key Results
- Two effective timescales — τfb(S) and τdiss(S) — defined operationally for any feedback-maintained structure at a chosen descriptive level.
- The persistence number Π — a dimensionless ratio analogous to the Damköhler or Péclet numbers, partitioning parameter space into persistent (Π > 1) and transient (Π < 1) regimes.
- The CPP theorem — grounded in Freidlin–Wentzell theory: exponential lifetime scaling for Π > 1, diffusion floor for Π < 1, with analytic crossover near Π ≈ 1.
- The Πmin bottleneck — rigorously justified via minimum-action escape paths: in multi-mode systems, persistence is governed by the weakest mode.
- Chronodynamic dominance condition (CDom) — identifies when the timescale balance is the binding constraint on persistence, versus resource depletion, structural instability, or mode coupling.
- Three-tier measurement protocols — from directly controllable engineered systems through complex biological systems, with a worked E. coli heat shock example.
- Thermodynamic learning efficiency ηL — a Landauer-normalised benchmark connecting information gain to energetic cost.