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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

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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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