A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which have different temperatures is investigated in the quantum mechanical framework. We study how they go to a thermal equilibrium. Time dependence of the temperature of the object is numerically studied and the difference of the time dependence between classical objects and quantum objects is clearly pointed out
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