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DY: Fachverband Dynamik und Statistische Physik
DY 27: Statistical Physics far from Thermal Equilibrium - Part I
DY 27.1: Invited Talk
Wednesday, March 18, 2015, 09:30–10:00, BH-N 334
On the use and abuse of thermodynamic entropy — Peter Hänggi1, Joern Dunkel3, and •Stefan Hilbert2 — 1Institute of Physics, University Augsburg, D-86135 Augsburg — 2Exzellenzcluster Universe, Boltzmannstr. 2, D-85748 Garching — 3Dept. Mathematics, MIT, 77 Massachusetts Avenue E17-412, Cambridge, MA 02139-4307 USA
Let us elaborate on the notion of thermodynamic entropy S (Clausius 1865) and its consequences. Gibbs put forward two notions of entropy for isolated systems that I commonly will refer to here as the volume entropy (involving the integrated density of states) and as the surface entropy, being proportional to the density of states, commonly also (incorrectly) known as the Boltzmann entropy. The absolute temperature, T= ∂ U/ ∂ S, is related to thermodynamic entropy; but which one to use? – The consistency for thermodynamics, i.e. the validity for the celebrated 0-th, 1-st and 2-nd thermodynamic Law singles out the Gibbs-entropy [1].
I shall address shortcomings that relate to the thermodynamics of small systems when sticking to the (Boltzmann)-surface entropy [1-2]. This criticism applies also to the use of absolute negative temperatures in systems with an upper bound in energy, occurring in experiments in spin systems or experiments involving isolated ultra-cold atomic gases.
[1] S. Hilbert, P. Hänggi, and J. Dunkel, Thermodynamic Laws in Isolated Systems, Phys. Rev. E 90, 062116 (2014).
[2] J. Dunkel and S. Hilbert, Phase transitions in small systems: microcanonical vs. canonical ensembles, Physica A 370, 390 (2006).