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Towards Boltzmann Distribution

The Boltzmann distribution (the most probable distribution) is one of the most important concepts used in physics, chemistry and biology. Suppose we put the system initially in one of the less probable state then the system will find the most probable state by a random search among all possible energy distributions and thus can take long time depending on the size of the system. In the following, simple analysis using our simple model shows that a small and physically reasonable energy bias against locally unfavorable energy distribution, of the order of a few $kT$, can reduce the time-scale of the process by a significant size.