The paper by Hal Tasaki explores the emergence of macroscopic irreversibility in a quantum system, specifically a free fermion chain with uniform nearest-neighbor hopping. The study focuses on the evolution of the system from an arbitrary initial state with a fixed macroscopic number of particles. The main result is that, at sufficiently large and typical times, the coarse-grained density distribution of the system becomes almost uniform with a probability extremely close to one. This establishes a ballistic diffusion, which is an irreversible behavior, in a system governed by quantum mechanical unitary time evolution. The key innovation in the proof is the justification of the strong ETH (Energy Eigenstate Thermalization Hypothesis) in the large-deviation form. This hypothesis states that the system approaches a thermal state for any energy eigenstate, even without introducing randomness to the initial state or the Hamiltonian. The proof relies on the absence of degeneracy in the many-body spectrum and a strong ETH bound, which are essential ingredients specific to the free fermion chain. The paper also discusses the fundamental difference between classical and quantum irreversibility. In classical systems, irreversibility often requires randomness in the initial state or Hamiltonian, whereas in quantum systems, it can be observed even without such randomness. The authors provide a rigorous example of equilibration in a free fermion chain, highlighting the importance of the strong ETH in understanding the long-time behavior of isolated macroscopic quantum systems.The paper by Hal Tasaki explores the emergence of macroscopic irreversibility in a quantum system, specifically a free fermion chain with uniform nearest-neighbor hopping. The study focuses on the evolution of the system from an arbitrary initial state with a fixed macroscopic number of particles. The main result is that, at sufficiently large and typical times, the coarse-grained density distribution of the system becomes almost uniform with a probability extremely close to one. This establishes a ballistic diffusion, which is an irreversible behavior, in a system governed by quantum mechanical unitary time evolution. The key innovation in the proof is the justification of the strong ETH (Energy Eigenstate Thermalization Hypothesis) in the large-deviation form. This hypothesis states that the system approaches a thermal state for any energy eigenstate, even without introducing randomness to the initial state or the Hamiltonian. The proof relies on the absence of degeneracy in the many-body spectrum and a strong ETH bound, which are essential ingredients specific to the free fermion chain. The paper also discusses the fundamental difference between classical and quantum irreversibility. In classical systems, irreversibility often requires randomness in the initial state or Hamiltonian, whereas in quantum systems, it can be observed even without such randomness. The authors provide a rigorous example of equilibration in a free fermion chain, highlighting the importance of the strong ETH in understanding the long-time behavior of isolated macroscopic quantum systems.