Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Poster Session I

DY 6.1: Poster

Monday, March 22, 2010, 16:00–18:00, Poster B2

Statistics of distinguishable particles and resolution of the Gibbs paradox of the first kind — •Hjalmar Peters — Universität Karlsruhe

In physics, there are two distinct paradoxes, which are both known under the name of "Gibbs paradox". In the following, the spurious increase in entropy when combining two gases of the same kind will be referred to as the Gibbs paradox of the first kind (GP1). The GP1 only arises if the gases consist of distinguishable particles. The analysis of the GP1 shows that, for systems of distinguishable particles, it is generally uncertain of which particles they consist. For the statistical description of a system of distinguishable particles, an underlying set of particles, containing all particles that in principle qualify for being part of the system, is assumed to be known. Of which elements of this underlying particle set the system is composed, differs from microstate to microstate. The uncertainty about the particle composition contributes to the entropy of the system. Systems for which admissible compositions with equal particle number are equiprobable will be called harmonic. Harmonic systems with the same underlying particle set are always correlated; hence, for harmonic systems, the entropy is no longer additive and loses its thermodynamic meaning. A quantity derived from entropy is introduced, the reduced entropy, which, for harmonic systems, replaces the entropy as thermodynamic potential. It can be shown that distinguishable and indistinguishable identical classical particles are physically equivalent. The resolution of the GP1 is demonstrated applying the previously found results.