We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first-order or second-order phase transition. The relaxation time to the equilibrium state, the Poincare cycles of the equilibrium state and the most far-from-equilibrium state, and the duration time of the states during first-order phase transition are calculated. It was shown that the scaling behavior of the Poincare cycles could be

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... ed as an indication to the nature of phase transition, and the ratio of duration time of the states could be a strong evidence of the metastability during first-order phase transition.