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We study the quantum many-body dynamics and the entropy production triggeredby an interaction quench in a system of $N=10$ interacting identical bosons inan external one-dimensional harmonic trap. The multiconfigurationaltime-dependent Hartree method for bosons (MCTDHB) is used for solving thetime-dependent Schr\"odinger equation at a high level of accuracy. We considermany-body entropy measures such as the Shannon information entropy, number ofprincipal components, and occupation entropy that are computed from thetime-dependent many-body basis set used in MCTDHB. These measures quantifyrelevant physical features such as irregular or chaotic dynamics, statisticalrelaxation and thermalization. We monitor the entropy measures as a function oftime and assess how they depend on the interaction strength. For largerinteraction strength, the many-body information entropy approaches the valuepredicted for the Gaussian orthogonal ensemble of random matrices and impliesstatistical relaxation. The basis states of MCTDHB are explicitlytime-dependent and optimized by the variational principle in a way thatminimizes the number of significantly contributing ones. It is therefore anon-trivial fact that statistical relaxation prevails in MCTDHB computations.Moreover, we demonstrate a fundamental connection between the production ofentropy, the build-up of correlations and loss of coherence in the system.Since the coherence and correlations are experimentally accessible, theirpresent connection to many-body entropies can be scrutinized to detectstatistical relaxation. Our results are the first ones obtained forthermalization of finite quantum systems using an optimized time-dependent andgenuinely many-body basis set.

Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons