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

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Abstract

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
Creators:	Creators Email ORCID Versteegh, Marijn A.M. m.a.m.versteegh@uu.nl Dieks, Dennis d.dieks@uu.nl
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 12:27
Last Modified:	17 Dec 2010 12:27
Item ID:	8432
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date:	3 December 2010
URI:	https://philsci-archive.pitt.edu/id/eprint/8432

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