The paper by Mark Srednicki explores the phenomenon of *eigenstate thermalization* in quantum systems, particularly focusing on a rarefied hard-sphere gas. The key idea is that if the energy eigenfunctions of a quantum system obey *Berry's conjecture*, which posits that these eigenfunctions behave like gaussian random variables, then the system will approach thermal equilibrium. This conjecture is expected to hold for systems with classical chaos, such as the hard-sphere gas. Srednicki reviews evidence supporting Berry's conjecture and demonstrates that previously overlooked effects strengthen its validity. He shows that an energy eigenstate satisfying Berry's conjecture predicts a Maxwell–Boltzmann, Bose–Einstein, or Fermi–Dirac distribution for the momentum of each particle, depending on the symmetry of the wave functions. This phenomenon is called *eigenstate thermalization*. The paper also discusses the decay of nonthermal features in the initial distribution of momenta, which occurs at least as fast as $O(\hbar/\Delta)t^{-1}$, where $\Delta$ is the uncertainty in the total energy. This result holds for individual initial states without the need for ensemble averaging, a contrast to classical statistical mechanics. Srednicki concludes that these findings provide a new foundation for quantum statistical mechanics, showing that quantum systems can thermalize even without interaction with an external heat bath. The paper includes numerical evidence supporting Berry's conjecture and discusses the role of "scars" in quantum chaos, which do not significantly alter the conclusions.The paper by Mark Srednicki explores the phenomenon of *eigenstate thermalization* in quantum systems, particularly focusing on a rarefied hard-sphere gas. The key idea is that if the energy eigenfunctions of a quantum system obey *Berry's conjecture*, which posits that these eigenfunctions behave like gaussian random variables, then the system will approach thermal equilibrium. This conjecture is expected to hold for systems with classical chaos, such as the hard-sphere gas. Srednicki reviews evidence supporting Berry's conjecture and demonstrates that previously overlooked effects strengthen its validity. He shows that an energy eigenstate satisfying Berry's conjecture predicts a Maxwell–Boltzmann, Bose–Einstein, or Fermi–Dirac distribution for the momentum of each particle, depending on the symmetry of the wave functions. This phenomenon is called *eigenstate thermalization*. The paper also discusses the decay of nonthermal features in the initial distribution of momenta, which occurs at least as fast as $O(\hbar/\Delta)t^{-1}$, where $\Delta$ is the uncertainty in the total energy. This result holds for individual initial states without the need for ensemble averaging, a contrast to classical statistical mechanics. Srednicki concludes that these findings provide a new foundation for quantum statistical mechanics, showing that quantum systems can thermalize even without interaction with an external heat bath. The paper includes numerical evidence supporting Berry's conjecture and discusses the role of "scars" in quantum chaos, which do not significantly alter the conclusions.