Probability distribution time periodic potentials

Due to thermal movement of the solvent molecules in the solvation shell, the potential energy of the reduced and oxidized species may deviate from their equilibrium value. If we could probe the energy of an individual species over a sufficiently long time period, we would find a distribution in its energy around the minimum. The probability that the energy of the oxidized and reduced species deviates from the equilibrium value by E(p) - E is given by the Boltzmann distribution ... 

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