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A form of nonequilibrium dynamics for a macroeconomic system is developed, in which each of the economic subjects working as interdependent decisionmakers acts so as to maintain the balance between the incoming and the outgoing monetary flows, except at the central bank. The nonequilibrium dynamics, which is based upon the balancing of monetary flows at every instantaneous time at each economic subject except the central bank, is described as a stochastic process since an outside observer cannot know or tell the reasons for particular choices on the part of the interdependent decisionmakers. A sample trajectory of the evolutionary process can be traced by referring only to the initial condition of the macroeconomic system at an arbitrary initial time, exhibiting a distinct contrast to those of various econometric models in which knowledge of the past history over a long period is needed for making a prediction of the future. The macroeconomic system evolves in the direction along which the ratio of the total material dissipation rate per unit time to the total material stock present in the system, both measured in common units of currency, decreases with time on a macroscopic time scale, even if some of the economic subjects undergo bankruptcies during the course of time evolution.