Bouchaud's trap model: exponential density of traps ρ(E) ~ e^{E/T_g}. Escape rate ~ e^{-E/T}. For T<T_g, mean waiting time diverges → aging. The system never equilibrates and memory of preparation persists forever.
Age (sim time): 0
Current trap E: —
Wait time τ = —
⟨E⟩(t) = —
T/T_g: —
Aging: —
⟨τ⟩ = —
ρ(E) ~ exp(E/T_g) (exponential)
τ_escape ~ exp(E/T)
For T<T_g: ⟨τ⟩=∫τρ(τ)dτ → ∞
p(τ) ~ τ^{−(1+T/T_g)}
Power law! (Lévy flight in time)
⟨E⟩(t) — never reaches equilibrium for T<T_g (aging!)