Cognitive Scaffold

Preparing your thinking workspace

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MENTAL MODEL · M5715

Gibbs Paradox

Gibbs Paradox
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

If two identical gases are mixed, does entropy increase? Classical mechanics suggests it should increase (because particle trajectories differ), but thermodynamics argues it should not (because the macroscopic state is unchanged). Quantum mechanics resolves this through the indistinguishability of identical particles.

SCAFFOLDING EFFECT

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The essence of distinction. If two things are completely indistinguishable in function and nature (identical), then exchanging them to create a 'new combination' is meaningless (entropy unchanged). Innovation must be based on differences; without differences, there is no increment in information.

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Entropy measures the number of microstates of a system. If two bottles of identical gas are mixed, classical statistics assumes particles are distinguishable and calculates an entropy increase (paradox); but real particles (identical) are indistinguishable, so the number of microstates before and after mixing is unchanged, hence entropy is unchanged. The key is 'distinguishability': only mixing distinguishable components increases entropy/information. Transferring to general thinking: repetition without difference produces no new information.

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Source support: Explicit

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    zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%90%89%E5%B8%83%E6%96%AF%E6%82%96%E8%AE%BAZH · Explicit
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