The entropy of a single large finite system undergoing both heat and work transfer

Computing the entropy of a system from a single trajectory is discussed when the energy exchange with the environment includes both mechanical and thermal terms. The physical example chosen as an illustration is a cluster of atoms impacting a hard surface. Each atom of the cluster interacts with the smooth surface by a momentum transfer using the hard cube model E. K. Grimmelmann, J. C. Tully and M. J. Cardillo, J. Chem. Phys. 72, 1039 (1980)]. Because of the thermal motion of the surface atoms the atoms of the cluster rebound from the surface with a (random) thermal component to their momentum. The change in the internal energy of the cluster has therefore both a mechanical, work, term and a heat transfer and the heat term contributes to the change in entropy of the cluster but the major contribution is the loss of potentially available work.