5D Library › Books › 5DL-B-013
行动的经典与统计力学
心理惯性、静摩擦阈值、双势阱克莱默斯逃逸率与习惯相变的数学模型及东方工夫论并读
Classical and Statistical Mechanics of Human Action: Psychological Inertia, Static Friction Thresholds, Kramers Escape Rate in Double-Well Potentials and Habit Phase Transitions, Read Beside East Asian Philosophy of Practice
DOI10.5281/zenodo.23738774摘要
为什么开始比继续难？为什么短促的爆发很少带来持久的改变？为什么半途而废会滑回原处？本书借用经典力学与统计力学的方程思考这些问题，并始终把物理本身的结论与把它们用于人时的跨学科类比或简化模型分开。各章依次考察：维持原状偏差与默认选项的证据，以及一个阻尼回复模型（只有持续的力才移动平衡点）和一个切换成本模型；库仑静摩擦与动摩擦、粘滑运动与接触老化，以及车轮牵引——核对后指出前进需要的是「抓地力」而不是「阻力」，库仑模型中也不存在「适度」的最佳摩擦；双势阱中的过阻尼朗之万方程与克莱默斯逃逸率，模拟显示降低势垒会同时加速出发与复发，而持续外力能缩短出发、延长复发，但撤掉即失效；尖点模型中的鞍结分岔、滞后与临界慢化；为教而学的证据（效应量 g 约 0.35–0.56）与复杂传染的网络模型，并证明「辅导两名同伴达标才能解锁」在封闭班级里必然阻塞，只有以辅导时段计数的版本可行，且封闭班级中不存在指数级传播；自我损耗效应在大规模预注册重复中几乎消失，以及动机重分配与机会成本的解释。
八章与《周易》「天行健」、王阳明《传习录》「人须在事上磨」和《碧岩录》「大死底人却活」公案并读，并说明类比的限度；最后给出一份四步势垒核查表（启动摩擦、势垒高度、外部棘轮、反馈延迟），以及一项比较独自学习与「完成两次同伴辅导才能解锁」的预注册随机对照试验方案（30 天完课率与盲评测验成绩为共同主要结局，每组 469 人，判定规则写成代码）。书中以标注框区分已发表的证据、可运行的 Python 计算（15 段程序，全部运行核对）、原典与作者的假说。本书不是心理治疗或医疗建议，不作任何诊断或疗效声称。
关键词：维持原状偏差；默认效应；静摩擦；动摩擦；粘滑运动；牵引力；双势阱；克莱默斯逃逸率；朗之万方程；滞后；鞍结分岔；为教而学；门生效应；复杂传染；自我损耗；习惯形成
Abstract
Why is starting harder than continuing? Why do short bursts rarely bring lasting change? Why does giving up halfway slide us back? This book uses the equations of classical and statistical mechanics to think about these questions, always keeping the conclusions of physics itself apart from their use on people as cross-disciplinary analogies or simplified models. The chapters examine in turn: the evidence on status quo bias and defaults, with a damped restoring model (only a sustained force moves the resting point) and a switching-cost model; Coulomb static and kinetic friction, stick-slip motion, contact aging and wheel traction — showing, after checking, that moving forward needs grip, not resistance, and that the Coulomb model has no "moderate" optimum of friction; the overdamped Langevin equation and Kramers' escape rate in a double well, where simulation shows that lowering the barrier speeds both leaving and relapse, while a steady outside pull shortens leaving and lengthens relapse but fails as soon as it is removed; the saddle-node bifurcation, hysteresis and critical slowing down of the cusp model; the evidence on learning by teaching (effect sizes g of about 0.35–0.56) and network models of complex contagion, with a proof that "tutor two classmates until they pass before unlocking" must jam a closed class, that only a version counted by tutoring sessions is workable, and that a closed class cannot spread exponentially; and the near-disappearance of ego depletion in large pre-registered replications, with explanations based on motivational reallocation and opportunity cost.
The eight chapters are read beside the Book of Changes ("Heaven moves vigorously"), Wang Yangming's Instructions for Practical Living ("a person must be polished in affairs") and the Blue Cliff Record case of "the one who has died the great death coming back to life", with the limits of each analogy, and end with a four-step barrier audit (start-up friction, barrier height, outside ratchet, feedback delay) and a pre-registered randomised controlled trial comparing solo study with a rule requiring two peer-tutoring sessions to unlock each stage (30-day completion and a blind-marked test score as co-primary outcomes, 469 per arm, with the decision rule written as code). Marked boxes separate published evidence, runnable Python calculations (15 programs, all run and checked), classical sources and the author's hypotheses. This book is not psychotherapy or medical advice and makes no diagnostic or therapeutic claim.
Keywords: status quo bias; default effect; static friction; kinetic friction; stick-slip; traction; double-well potential; Kramers escape rate; Langevin equation; hysteresis; saddle-node bifurcation; learning by teaching; protégé effect; complex contagion; ego depletion; habit formation
目录 · Contents
- 序：为什么开始比继续难English 中文Preface: Why Starting Is Harder than Continuing
- 第一章 惯性与维持原状English 中文Chapter 1 Inertia and the Status Quo
- 第二章 静摩擦与动摩擦English 中文Chapter 2 Static and Kinetic Friction
- 第三章 双势阱与克莱默斯逃逸率English 中文Chapter 3 The Double Well and Kramers' Escape Rate
- 第四章 滞后与临界点English 中文Chapter 4 Hysteresis and Tipping Points
- 第五章 社会耦合与「教中学」English 中文Chapter 5 Social Coupling and Learning by Teaching
- 第六章 认知能量预算与自我损耗之争English 中文Chapter 6 The Cognitive Energy Budget and the Ego-Depletion Debate
- 第七章 东方工夫论原典并读English 中文Chapter 7 East Asian Philosophy of Practice
- 第八章 实践与预注册试验English 中文Chapter 8 Practice and a Pre-Registered Trial
How to cite · 引用
Fan, Y. (2026). Classical and Statistical Mechanics of Human Action: Psychological Inertia, Static Friction Thresholds, Kramers Escape Rate in Double-Well Potentials and Habit Phase Transitions, Read Beside East Asian Philosophy of Practice [行动的经典与统计力学] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23738774
BibTeX
@book{fan2026mechanics,
title = {{Classical and Statistical Mechanics of Human Action}: Psychological Inertia, Static Friction Thresholds, Kramers Escape Rate in Double-Well Potentials and Habit Phase Transitions, Read Beside East Asian Philosophy of Practice},
author = {Fan, Yafu},
year = {2026},
publisher = {5D Library},
edition = {Version 1.0.0},
doi = {10.5281/zenodo.23738774},
url = {https://doi.org/10.5281/zenodo.23738774},
note = {Chinese title: 行动的经典与统计力学}
}
| DOI | https://doi.org/10.5281/zenodo.23738774 |
|---|---|
| DOI（全部版本 all versions） | https://doi.org/10.5281/zenodo.23738773 |
| ORCID | https://orcid.org/0009-0004-3519-1203 |
| 5D Library ID | 5DL-B-013 |
| 版本 Version | 1.0.0 · 中英双语版 Bilingual edition |
| 出版日期 Date | 2026-10-28 |
| 网址 Online | https://5dlibrary.com/books/mechanics-of-action/ |
| SHA-256 · mechanics-of-action_bilingual_v1.0.0.pdf | e5cf378fda1f8e529bc70d4cff1e6c0cedd5f787bfd165ed46ae775068274123 |
| SHA-256 · mechanics-of-action_en_v1.0.0.pdf | adf6b5d1a20544a0ebfafaa324bd6e019bd0287b1e14637397f722515a6b17ed |
| SHA-256 · mechanics-of-action_zh_v1.0.0.pdf | cc9802f9ef81edff3e6565647a82d58ecd9e381a8085b1e2bb18bea02dcb11ed |
| Licence · 许可 | Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Disclosure. The author uses this book as the methodological basis of his community cognition courses, 5D Ascension Cards (Dimensional Shift Card Decks) and the Yafu AI knowledge base, and so has a direct commercial interest in its subject and in the result of the Chapter 8 trial. The book promotes no course, card deck or product and makes no health or therapeutic claim; the trial is designed to be run and analysed by researchers independent of the author's business; all the code and the study protocol are published openly for anyone to check.