From coherent quasi-irreversible quantum dynamics towards the second law of thermodynamics: The model boron rotor B13+

The planar boron cluster B13+ provides a model to investigate the microscopic origin of the second law of thermodynamics in a small system. It is a molecular rotor with an inner wheel that rotates in an outer bearing. The cyclic reaction path of B13+ passes along thirty equivalent global minimum structures (GMi, i = 1, 2, ..., 30). The GMs are embedded in a cyclic thirty-well potential. They are separated by thirty equivalent transition states with potential barrier Vb. If the boron rotor B13+ is prepared initially in one of the thirty GMs, with energy below Vb, then it tunnels sequentially to its nearest, next-nearest etc. neighbors (520 fs per step) such that all the other GMs get populated. As a consequence, the entropy of occupying the GMs takes about 6 ps to increases from zero to a value close to the maximum value for equi-distribution. Perfect recurrences are practically not observable.