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As recently manifested , the quench dynamics of isolated quantum systemsconsisting of a finite number of particles, is characterized by an exponentialspreading of wave packets in the many-body Hilbert space. This happens when theinter-particle interaction is strong enough, thus resulting in a chaoticstructure of the many-body eigenstates considered in an unperturbed basis. Thesemi-analytical approach used here, allows one to estimate the rate of theexponential growth as well as the relaxation time, after which theequilibration (thermalization) emerges. The key ingredient parameter in thedescription of this process is the width $\Gamma$ of the Local Density ofStates (LDoS) defined by the initially excited state, the number of particlesand the interaction strength. In this paper we show that apart from the meaningof $\Gamma$ as the decay rate of survival probability, the width of the LDoS isdirectly related to the diagonal entropy and the latter can be linked to thethermodynamic entropy of a system equilibrium state emerging after the completerelaxation. The analytical expression relating the two entropies is derivedphenomenologically and numerically confirmed in a model of bosons with randomtwo-body interaction, as well as in a deterministic model which becomescompletely integrable in the continuous limit.

Process of equilibration in many-body isolated systems: Diagonal versus thermodynamic entropy