Thermodynamic laws in isolated systems

TL;DR

This paper analyzes different microcanonical entropy definitions in isolated quantum systems, demonstrating that only the Gibbs volume entropy consistently satisfies all fundamental thermodynamic laws.

Contribution

It provides a detailed comparison of microcanonical entropy definitions, establishing that the Gibbs volume entropy uniquely complies with the zeroth, first, and second laws.

Findings

Gibbs volume entropy satisfies all three thermodynamic laws

Most other entropy definitions violate at least one law

Analysis is based on exact results and tractable examples

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.