Entropy Arrow — DOT
A Structural Analogy, Not a Physical Claim

Entropy Arrow
Universe Scale & Agent Scale

Thermodynamic entropy (Boltzmann, 1877) defines the arrow of time: S = kB ln Ω. Kullback-Leibler divergence, a real, standard statistical measure, can define an analogous “arrow of authorization” — how far an agent’s observed behaviour has diverged from its declared intent distribution.

This is a structural analogy between two real mathematical concepts, not a claim that agent authorization and thermodynamic entropy are the same physical phenomenon. The comparison illustrates the shape of the idea, not a scientific equivalence.
The Correspondence
ConceptThermodynamicsIBA Authorization
The primitiveBoltzmann entropy, SKL-divergence, DKL
Declared stateLow-entropy initial conditionsSigned intent certificate at issuance
DirectionArrow of timeArrow of authorization — aligned to drifted
What growsDisorderDivergence from declared intent
RecordFossil record, cosmic background radiationAudit chain (illustrated as WitnessBound)
Live Simulation
0.00KL-Divergence
AUTHORIZEDGate Status
0Logged Events

Flag threshold and kill threshold below are illustrative values for this demo, not independently calibrated or benchmarked figures.

KL baseline: 0.00. Declared intent loaded.