V2EX phase space

Phase Space

Definition|释义

“相空间”:在物理学、动力系统与统计力学中,用来表示系统所有可能状态的抽象空间;每个点对应系统在某一时刻的完整状态(常见坐标为“位置与动量”等成对变量)。在量子与经典力学语境中都很常见。

Pronunciation|发音(IPA)

/fez spes/

Examples|例句

The pendulum’s motion can be represented in phase space.
钟摆的运动可以在相空间中表示出来。

In chaotic systems, nearby trajectories in phase space can diverge rapidly even with tiny differences in initial conditions.
在混沌系统中,即使初始条件只有极小差异,相空间中相近的轨迹也可能迅速发散。

Etymology|词源

phase 来自希腊语 phasis(“显现、阶段”),space 来自拉丁语 spatium(“空间、距离”)。合在一起的 phase space 属于近代科学术语,用“空间”的比喻把系统的“所有状态”统一放进一个几何框架中,便于用轨迹、流形、体积等概念来分析演化规律。

Related Words|相关词汇

Literary Works|作品中的用例

  • The Feynman Lectures on Physics(费曼《物理学讲义》):在经典力学与统计物理相关章节讨论相空间与相轨迹。
  • Mechanics(Landau & Lifshitz,《理论物理学教程力学》):用相空间与哈密顿形式系统化描述运动。
  • Nonlinear Dynamics and Chaos(Strogatz,《非线性动力学与混沌》):用相图/相空间直观呈现非线性系统行为。
  • Chaos: Making a New Science(James Gleick,《混沌:开创新科学》):科普叙述中频繁借助“相空间轨迹”等概念解释混沌现象。
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