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We discuss in detail statistical mechanical properties of quantum dynamics with the use of numerical simulations of isolated one-dimensional spin systems of various sizes. With respect to the energy distribution in a subsystem, a good agreement is observed between those obtained by the method of statistical mechanics and via long-time average over simulation, even in the system composed of a small number of spins. In particular, the distribution of energy forms the canonical distribution.

We extend the derivation of the finite-size Kubo formula for classical systems by Kundu et al. to a finite open quantum system in contact with reservoirs. Starting with the master equation obtained from the quantum repeated interaction model, we examine the linear response, utilizing superoperators defined by virtue of a conservation law. Some generalizations of our method are also discussed.