Thermodynamic laws in isolated systems

2014/08/31 by Stefan Hilbert, Peter Hänggi, Jörn Dunkel · 2 citations
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.90.062116

published as Phys. Rev. E 90: 062116 (2014) · footnotes 19, 26 and outlook section added

arxiv created 2014/11/22 · arxiv updated 2015/01/05

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, focussing specifically on whether they satisfy or violate the zeroth, first and second law 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.

Cited by

• The specific heat anomaly stems from a third-order phase transition in the 2D lattice sine-Gordon model
• Virtual temperatures as a key quantifier for passive states in quantum thermodynamic processes

Related

• Comparison of canonical and microcanonical definitions of entropy
• Resolving the Debate between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures
• Microcanonical entropy: consistency and adiabatic invariance
• Microcanonical analysis of Boltzmann and Gibbs Entropies in trapped cold atomic gases
• Construction of microcanonical entropy on thermodynamic pillars