V2EX ergodicity

Ergodicity

Definition / 定义

遍历性(或遍历性质):指一个系统在足够长时间内的“时间平均”与在所有可能状态上的“总体/系综平均”相一致的性质。常见于概率论、统计物理、动力系统等领域。
(该词也可在不同学科中有更具体的技术性定义。)

Pronunciation / 发音

/dsti/

Examples / 例句

Many statistical models assume ergodicity.
许多统计模型都假设系统具有遍历性。

If the process has ergodicity, the long-run time average of an observable can match its ensemble average.
如果该过程具有遍历性,那么某个观测量的长期时间平均可以与其系综平均相一致。

Etymology / 词源

ergodicity 来自 ergodic(遍历的)加名词后缀 -ity(表示“性质、状态”)。ergodic 源自希腊语词根:ergon(“工作、作用”)与 hodos(“道路、路径”)的组合,早期用于描述系统在其“状态空间路径”上的运动特征,后来在统计物理与动力系统中固定为“遍历性”的核心概念。

Related Words / 相关词

Literary Works / 作品例证

  • **Ergodic Theory and Dynamical Systems**(教材/专著领域常见标题,讨论遍历性与相关定理)
  • **An Introduction to Ergodic Theory**(Peter Walters,经典入门书,系统讲解遍历性)
  • **Statistical Mechanics**(如 R. K. Pathria 等教材版本,常在“遍历假设/遍历性”处使用该词)
  • **Chaos: Making a New Science**(James Gleick,科普写作中涉及混沌与动力系统背景时可能提及遍历相关概念)
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