Cognitive Scaffold

Preparing your thinking workspace

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MENTAL MODEL · M5825

FPU Problem

FPU Problem
SystemsHigh supportSystems Theory
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Updated 2026-08-05

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INTRODUCTION

English translation pending.

CORE DEFINITION

A numerical experiment conducted in 1954 by Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou, in which a one-dimensional chain of weakly nonlinear oscillators was simulated in the expectation that energy would equipartition across all modes. Instead the energy returned almost entirely to the initial modes after a recurrence time. The core claim is that nonlinear systems may fail to equilibrate over long periods. The qualification is that the result concerns a specific weak nonlinearity, and later work showed that stronger coupling does eventually thermalize.

SCAFFOLDING EFFECT

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- Use Equilibration Check: Test whether a system actually mixes rather than assuming that it will even out on its own. - Use Locked-Structure Search: Look for local structures that hold resources instead of distributing them. - Use Recurrence Watch: Watch for periodic return of energy to its starting configuration rather than gradual dissipation.

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In a weakly nonlinear system, the coupling between modes is too weak to spread energy across the full spectrum within the observed time, so energy transfers among a small number of modes and then returns to where it started. Because the nonlinearity is small, the system behaves almost like a set of independent oscillators with slow exchange, and thermal equilibrium is not reached. Stronger nonlinearity restores mixing, which is why the result describes a regime rather than a universal rule.

MINIMUM ACTION

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problemZH · Explicit
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