Governing Equations

Transit Temperature Profile:
  T(t) = T_ambient + (T_initial - T_ambient) · exp(-t/τ)
  where τ = thermal time constant (depends on insulation)

Ice Melting Phase:
  T(t) = 0°C while ice present (latent heat absorption)
  After ice exhaustion: T(t) rises exponentially

Stability Budget Burn Rate:
  dB/dt = (T(t) - T_spec) when T(t) > T_spec
  B_remaining = B_initial - ∫ max(0, T(t) - T_spec) dt

Arrhenius Stability Budget:
  k_eff = k_25°C · exp[(Ea/R) · (1/298 - 1/T(t))]
  Budget burn = Σ k_eff · Δt

GDP Compliance:
  Pass: T(t) ≤ T_spec for >95% of transit time
  Excursion: T(t) > T_spec for >5% of transit time
  Critical: T(t) > T_spec for >30 min continuous

Excursion Mapping:
  Time-weighted average temperature (TWAT)
  TWAT = Σ(T_i · Δt_i) / ΣΔt_i