我们证明：任何具有严格正转移概率且存在平稳伯努利测度的随机元胞自动机（PCA）均呈指数遍历性；此外，此类系统中任意有限区域的混合时间与其直径呈对数关系。类似结论在连续时间情形下亦成立，适用于正率、有限作用范围的相互作用粒子系统（IPS）。证明借助熵方法，并依赖于将系统表示为带噪声系统的扰动这一技巧。其遍历行为源于两类效应的竞争：一是由噪声导致的随机性累积，二是由局部信息交换导致的随机性扩散。我们进一步证明，在二维及更高维情形下， admitting 平稳伯努利测度的正率随机元胞自动机在算法上无法与不 admitting 平稳伯努利测度者相区分。

We prove that every probabilistic cellular automaton with strictly positive transition probabilities that admits a stationary Bernoulli measure is exponentially ergodic. Moreover, the mixing time of any finite region in such a system is logarithmic in the diameter of the region. A similar result holds in continuous time for positive-rate, finite-range interacting particle systems. The proofs use entropy, and rely on a representation of the system as a perturbation of another system with noise. The ergodic behaviour results from a competition between the accumulation of randomness due to noise and the diffusion of randomness due to local information exchange. We show that, in two and higher dimensions, the positive-rate probabilistic cellular automata that admit stationary Bernoulli measures are algorithmically indistinguishable from those that do not.