Ergodicity Breaking in Anomalous Diffusion

Time-averaged MSD (δ²) vs ensemble-averaged MSD ⟨x²⟩. For CTRW subdiffusion: time-avg MSD ~ T^{1-α} diverges while ensemble MSD ~ t^α — non-ergodic! For fractional Brownian motion (fBm): both coincide — ergodic.

0.50
15
800
⟨δ²⟩/⟨x²⟩:
Ergodicity breaking:
α_measured: