How does the N signify the indistinguishability in the Gibbs Paradox?

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Discussion Overview

The discussion revolves around the Gibbs Paradox and the role of the N! factor in statistical mechanics, particularly in relation to the indistinguishability of particles. Participants explore the implications of this concept for entropy calculations and the potential loss of information in the process.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that Gibbs introduced the N! to make entropy extensive and attributes it to the indistinguishability of particles.
  • Another participant explains that N distinguishable particles can be distributed over N locations in N! ways, while N indistinguishable particles can only be distributed in one way.
  • A side question is raised regarding whether any information is lost when dividing by N! in entropy calculations, with a focus on the implications in quantum mechanics.
  • A later reply suggests that any lost information is only spurious and does not represent physically existent information.

Areas of Agreement / Disagreement

Participants express differing views on the implications of using N! in entropy calculations, particularly regarding the loss of information, indicating that the discussion remains unresolved.

Contextual Notes

The discussion touches on assumptions regarding the nature of indistinguishability and the definition of information in the context of statistical mechanics and quantum mechanics, which may not be fully articulated.

annaphys
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Gibbs introduced the N! to then make S extensive. He then attributed the N! to the particles being indistinguishable. How does the N! signify the indistinguishability?
 
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You can distribute N distinguishable particles over N 'locations' in N! ways.
You can distribute N indistinguishable particles over N 'locations' in one way only.
 
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Nice. Thanks. That makes sense since in deriving the Entropy, we divide by N!. A side question. Are we losing any information of the system by doing this? Of course in quantum mechanics particles are indistinguishable but it'd be interesting to know if any information is lost.
 
annaphys said:
Are we losing any information of the system by doing this? Of course in quantum mechanics particles are indistinguishable but it'd be interesting to know if any information is lost.
Lost is only spurious information that is physically nonexistent anyway.
 
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