title: Thermodynamic laws in isolated systems.
abstract: The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics. Here we provide a detailed comparison of the most commonly considered microcanonical entropy definitions, focusing specifically on whether they satisfy or violate the zeroth, first, and second laws of thermodynamics. Our analysis shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws simultaneously. To avoid ambiguities, the discussion is restricted to exact results and analytically tractable examples.
authors.affiliation: Exzellenzcluster Universe, Boltzmannstr. 2, D-85748 Garching, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Hilbert
authors.affiliation: Institute of Physics, University of Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany and Nanosystems Initiative Munich, Schellingstr. 4, D-80799 München, Germany.
authors.forename: Peter
authors.initials: P
authors.lastname: Hänggi
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue E17-412, Cambridge, Massachusetts 02139-4307, USA.
authors.forename: Jörn
authors.initials: J
authors.lastname: Dunkel