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Starting from a classical mechanics of a ``colloid particle'' and $N$ ``watermolecules'', we study effective stochastic dynamics of the particle which jumpsbetween deep potential wells. We prove that the effective transitionprobability satisfies (local) detailed balance condition. This enables us torigorously determine precise form of the transition probability when barrierpotentials have certain regularity and symmetry.

Two theorems that relate discrete stochastic processes to microscopic mechanics