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MENTAL MODEL · M13095

Principle of minimum energy

Principle of minimum energy
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Updated 2026-08-13

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INTRODUCTION

English translation pending.

CORE DEFINITION

A thermodynamic equilibrium criterion: for a closed system whose entropy and external parameters are held constant, the stable equilibrium state is the one that minimizes internal energy. Because internal energy is a state function and is bounded below for a system of fixed composition, the reachable states always contain a lowest member. Under fixed entropy the second law permits only changes that do not reduce entropy, so energy decrease remains the only allowed direction of spontaneous change and equilibrium is reached where that gradient vanishes. It is the energy-based counterpart of the maximum entropy principle, which applies when energy rather than entropy is held fixed.

SCAFFOLDING EFFECT

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- Choosing a potential: Match the thermodynamic potential to whichever variables your constraints actually hold fixed. - Locating equilibrium: Predict the final state by asking which reachable configuration minimizes internal energy. - Reading direction: Treat spontaneous change as motion downhill in energy until no further decrease is possible.

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Internal energy is a state function with a lower bound, so among reachable states one is minimal. Holding entropy and external parameters fixed removes every other direction of allowed change, which leaves energy decrease as the only path the second law permits. The resulting energy gradient acts as a driving force, and equilibrium sits exactly where the gradient disappears, so the criterion predicts both the final state and the direction of approach.

MINIMUM ACTION

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