This paper presents a proof of macroscopic irreversibility in a free fermion chain under quantum mechanical unitary time evolution. The authors show that, starting from an arbitrary initial state with a fixed macroscopic number of particles, the system evolves to a state with almost uniform density at sufficiently large and typical times. This demonstrates that irreversible behavior, such as ballistic diffusion, can emerge in quantum systems without introducing randomness to the initial state or the Hamiltonian, unlike classical systems where irreversibility is often associated with randomness. The key idea is the justification of the strong ETH (energy eigenstate thermalization hypothesis) in the large-deviation form. The authors prove that the measured coarse-grained density distribution becomes almost uniform with quantum mechanical probability extremely close to one. This result is shown for a free fermion chain with N spinless fermions on a chain of length L, with periodic boundary conditions. The Hamiltonian is diagonalized in terms of plane wave states, and the energy eigenstates are shown to be non-degenerate under certain conditions. The paper also discusses the difference between classical and quantum irreversibility. While classical systems often require randomness to exhibit irreversibility, quantum systems can exhibit macroscopic irreversibility even with deterministic initial states. The authors demonstrate this by showing that the coarse-grained density distribution becomes uniform with high probability for any non-random initial state. The main results are Theorem 2 and Theorem 3, which show that the probability of the system being out of equilibrium decreases exponentially with the number of particles. The proof relies on the strong ETH bound, which is established through a series of technical lemmas. The authors also discuss the implications of their results for the understanding of thermalization in isolated quantum systems and the role of the ETH in this context. The paper concludes that the free fermion chain exhibits irreversible expansion for any initial state where the density differs from the equilibrium density.This paper presents a proof of macroscopic irreversibility in a free fermion chain under quantum mechanical unitary time evolution. The authors show that, starting from an arbitrary initial state with a fixed macroscopic number of particles, the system evolves to a state with almost uniform density at sufficiently large and typical times. This demonstrates that irreversible behavior, such as ballistic diffusion, can emerge in quantum systems without introducing randomness to the initial state or the Hamiltonian, unlike classical systems where irreversibility is often associated with randomness. The key idea is the justification of the strong ETH (energy eigenstate thermalization hypothesis) in the large-deviation form. The authors prove that the measured coarse-grained density distribution becomes almost uniform with quantum mechanical probability extremely close to one. This result is shown for a free fermion chain with N spinless fermions on a chain of length L, with periodic boundary conditions. The Hamiltonian is diagonalized in terms of plane wave states, and the energy eigenstates are shown to be non-degenerate under certain conditions. The paper also discusses the difference between classical and quantum irreversibility. While classical systems often require randomness to exhibit irreversibility, quantum systems can exhibit macroscopic irreversibility even with deterministic initial states. The authors demonstrate this by showing that the coarse-grained density distribution becomes uniform with high probability for any non-random initial state. The main results are Theorem 2 and Theorem 3, which show that the probability of the system being out of equilibrium decreases exponentially with the number of particles. The proof relies on the strong ETH bound, which is established through a series of technical lemmas. The authors also discuss the implications of their results for the understanding of thermalization in isolated quantum systems and the role of the ETH in this context. The paper concludes that the free fermion chain exhibits irreversible expansion for any initial state where the density differs from the equilibrium density.