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The Gibbs Paradox and the Distinguishability of Identical Particles

Versteegh, Marijn A.M. and Dieks, Dennis (2010) The Gibbs Paradox and the Distinguishability of Identical Particles. [Preprint]

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    Classical particles of the same kind (i.e., with the same intrinsic properties, so-called ``identical particles'') are distinguishable: they can be labeled by their positions (because of their impenetrability) and follow different trajectories. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and via S=k ln W this leads to a non-extensive expression for the entropy. This result is generally considered wrong because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency, notoriously illustrated by the Gibbs paradox, that identical particles must be treated as indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In this article we argue, by contrast, that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly all-right both from a theoretical and an experimental perspective. We remove the inconsistency with thermodynamics by pointing out that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. Finally, we observe that even identical quantum particles are in some cases distinguishable; and conclude that quantum mechanics is irrelevant to the Gibbs paradox.

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    Item Type: Preprint
    Keywords: Gibbs paradox, identical particles, entropy, indistinguishability, second law of thermodynamics
    Subjects: Specific Sciences > Physics > Fields and Particles
    Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
    Depositing User: Mr. Marijn A.M. Versteegh
    Date Deposited: 17 Dec 2010 07:27
    Last Modified: 17 Dec 2010 07:27
    Item ID: 8432

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