Extend qualitative findings to realistic quantum many‑body systems

Establish whether the qualitative behaviors reported for eleven microscopic entropy definitions (Boltzmann-surface, Gibbs-volume, canonical, coarse-grained observational, entanglement, diagonal types) and three temperature definitions (Boltzmann, Gibbs, canonical) in the banded random-matrix heat exchange model persist in realistic, non-integrable quantum many-body systems, in light of the eigenstate thermalization hypothesis.

Background

The paper models energy exchange between two systems using a banded random-matrix interaction and studies the time evolution of multiple entropy and temperature definitions. Random matrix theory is invoked as a minimal model for complex, non-integrable quantum systems, and the authors reference the eigenstate thermalization hypothesis (ETH) to motivate broader relevance.

While the numerical results are presented for this specific random-matrix setup, the authors explicitly conjecture that their qualitative findings should hold for more realistic quantum many-body systems, leaving open the task of establishing this rigorously or by direct simulation or experiment.