  In this paper, we propose a novel minimal physical model to elucidate the
long-term stochastic variability of blazars. The model is built on the
realistic background of magnetized plasma jets dissipating energy through a
turbulent cascade process that transfers energy to small-scale structures with
highly anisotropic radiation. The model demonstrates the ability to
spontaneously generate variability features consistent with observations of
blazars under uniformly random fluctuations in the underlying physical
parameters. This indicates that the model possesses self-similarity across
multiple time scales, providing a natural explanation for the universal power
spectral density (PSD) structure observed in different types of blazars.
Moreover, the model exhibits that when the cascade process produces a
relatively flat blob energy distribution, the spectral index of the
model-simulated PSD in the high-frequency regime will be steeper than that
predicted by the Damped Random Walk (DRW) model, which is in agreement with
recent observations of active galactic nucleus (AGN) variability, providing a
plausible theoretical explanation. The model is also able to reproduce the
observed fractional variability amplitude (FVA) characteristics of blazars, and
suggests that the specific particle acceleration and radiative cooling
processes within the blob may not be the key factor shaping the long-term
stochastic variability. This minimal model provides a new physical perspective
for understanding the long-term stochastic variability of blazars.
