Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 12: Statistical physics (general)

DY 12.2: Talk

Tuesday, March 27, 2007, 10:15–10:30, H3

Haar measures, relative entropy and the relativistic canonical velocity distribution — •Jörn Dunkel, Peter Talkner, and Peter Hänggi — Institut für Physik, Universität Augsburg, Theoretische Physik I, Universitätsstrasse 1, D-86135 Augsburg, Germany

The concept of equipartition (uniform distribution) can be extended to locally compact, topological groups by means of the Haar measure. Guided by this fact, we propose that the relative entropy with respect to the Haar measure of the Lorentz group provides the most natural choice for the canonical equilibrium entropy in relativistic thermostatistics. Maximization of this entropy under the usual constraints yields a modified one-particle Jüttner distribution that differs from the standard Jüttner distribution by a prefactor which is proportional to the inverse relativistic kinetic energy. The argument shows that only the modified distribution is consistent with the principle of Lorentz invariance, whereas the standard Jüttner function is not. The relevance of this result with regard to applications in high energy physics and astrophysics is discussed.