Entropy and temperature in finite isolated quantum systems

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.

Automated summary

We investigate the comparison between the temperature calculated from the microcanonical entropy and the canonical temperature for finite isolated quantum systems. Our focus is on systems that can be numerically diagonalized exactly due to their size. We thus characterize the deviations from ensemble equivalence at finite sizes and present multiple methods to compute the microcanonical entropy, providing numerical results for the entropy and temperature obtained using these methods. We show that using an energy window with a particular energy dependence minimizes the deviations from the canonical temperature.