| Abstract
| - We propose a mathematical treatment of the activated processes governed by stochastic Langevin dynamicswith a colored random force, corresponding to a noise generated by an Ornstein−Uhlenbeck process. Suchnon-Markovian dynamics take place in a variety of chemical and biological systems. Using the path integralapproach, we constructed the conditional probability for passing between two stationary states in configurationalspace. Our relations can be used for Monte Carlo sampling of evolution trajectories for systems with manydegrees of freedom as well as for determining the reaction coordinate used in transition state theory. On thebasis of our relation for a conditional probability, we generalize the method of determining the most probablepath to the case of colored random force. Using the simple three-hole potential, we examine numerically theeffect of nonzero correlation time (memory) on the evolution of the most probable path for a finite temperature.
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