(BOAP algorithm: BJ Leimkuhler and C Matthews Appl. Math. Res. eXpress 2013, 34–56 (2013); J. Chem. Phys. 138, 174102 (2013))
where:
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is the friction force. It simulates the effect of the bath (solvent) on the system.
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is the random force, which is represented by the derivate of a Wiener process 
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governs the strenght of the random force (it is related to the friction coefficient via the fluctuation-dissipation theorem)
With solution:
