This study investigates how quantum thermalization occurs in an isolated many-body system through entanglement. The research focuses on a Bose-Einstein condensate of rubidium atoms in a two-dimensional optical lattice, where quantum thermalization is observed. The system is described by the Bose-Hubbard model, which accounts for tunneling and interactions between particles. The experiment involves a quantum quench, where the system is suddenly perturbed, leading to the evolution of the quantum state. The study demonstrates that even though the full quantum state remains pure and has zero entropy, local entropy emerges due to quantum entanglement, allowing the system to exhibit thermal behavior. The researchers measure the entanglement entropy and find that it aligns with the thermal entropy in thermalization. They also observe that the local number statistics of the system converge to a thermal distribution, consistent with a canonical thermal ensemble. The study shows that the entanglement entropy grows with the size of the subsystem, following a volume law, which is a key feature of thermalization. The results support the Eigenstate Thermalization Hypothesis (ETH), which suggests that thermalization in isolated quantum systems can be explained by the properties of individual energy eigenstates. The study also highlights the role of entanglement in creating local entropy and enabling thermalization, even in a globally pure quantum state. The findings demonstrate that the local observables of a globally pure quantum state can mimic those of a thermal ensemble, indicating that the quantum state can be indistinguishable from a mixed thermal state. The study provides experimental evidence for the equivalence between entanglement entropy and thermal entropy, and shows that the dynamics of entanglement play a crucial role in thermalization. The results have implications for understanding the behavior of quantum systems and the emergence of thermal properties in isolated many-body systems.This study investigates how quantum thermalization occurs in an isolated many-body system through entanglement. The research focuses on a Bose-Einstein condensate of rubidium atoms in a two-dimensional optical lattice, where quantum thermalization is observed. The system is described by the Bose-Hubbard model, which accounts for tunneling and interactions between particles. The experiment involves a quantum quench, where the system is suddenly perturbed, leading to the evolution of the quantum state. The study demonstrates that even though the full quantum state remains pure and has zero entropy, local entropy emerges due to quantum entanglement, allowing the system to exhibit thermal behavior. The researchers measure the entanglement entropy and find that it aligns with the thermal entropy in thermalization. They also observe that the local number statistics of the system converge to a thermal distribution, consistent with a canonical thermal ensemble. The study shows that the entanglement entropy grows with the size of the subsystem, following a volume law, which is a key feature of thermalization. The results support the Eigenstate Thermalization Hypothesis (ETH), which suggests that thermalization in isolated quantum systems can be explained by the properties of individual energy eigenstates. The study also highlights the role of entanglement in creating local entropy and enabling thermalization, even in a globally pure quantum state. The findings demonstrate that the local observables of a globally pure quantum state can mimic those of a thermal ensemble, indicating that the quantum state can be indistinguishable from a mixed thermal state. The study provides experimental evidence for the equivalence between entanglement entropy and thermal entropy, and shows that the dynamics of entanglement play a crucial role in thermalization. The results have implications for understanding the behavior of quantum systems and the emergence of thermal properties in isolated many-body systems.