Classical small systems coupled to finite baths

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We have studied the properties of a classical Nₛ-body system coupled to a bath containing NB-body harmonic oscillators, employing an (Nₛ+NB) model which is different from most of the existing models with Nₛ=1. We have performed simulations for Nₛ-oscillator systems, solving 2(Nₛ+NB) first-order differential equations with Nₛ ≃ 1 - 10 and NB ≃ 10 - 1000, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence. Detailed calculations of the stationary energy distribution of the system fₛ(u) (u: an energy per particle in the system) have shown that its properties are mainly determined by Nₛ but weakly depend on NB. The calculated fₛ(u) is analyzed with the use of the Γ and q-Γ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where q stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the Nₛ-body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional (Nₛ+NB) models which include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.