Entropy and Temperature in finite isolated quantum systems

Abstract

We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact diagonalization. We thus characterize the deviations from ensemble equivalence at finite sizes. We describe multiple ways to compute the microcanonical entropy and present numerical results for the entropy and temperature computed in these various ways. We show that using an energy window whose width has a particular energy dependence results in a temperature with minimal deviations from the canonical temperature.

v2: Updated with changes made for publication in Phys. Rev. E. 10 pages, 7 figures. v1: 9 Pages, 6 Figures

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• Many-Body Localization in the Age of Classical Computing
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• Quantum master equation from the eigenstate thermalization hypothesis
• Fermionic Magic Resources of Quantum Many-Body Systems
• Resolving the Debate Between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures
• Many Body Density of States of a system of non interacting spinless fermions
• Taking the temperature of quantum many-body scars
• Direct temperature readout in nonequilibrium quantum thermometry