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

Abstract

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, 1039Phys. 72, (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.

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“…Ayelet Gross saw that the behavior of these large, energy-rich multiple-atom systems, a behavior generated by strict mechanical evolution, was as fully expected as it would be were there a hot macroscopic body cooling down irreversibly toward equilibrium (49). This enabled us to offer a purely mechanical definition of entropy (50). I believe this chapter is not closed yet.…”

Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

“…Here δ Q(t) is the instantaneous heat exchange of the system with the B, δ Q (t) is the instantaneous "uncompensated heat" due to internal nonequilibrium processes, and T (t) is the instantaneous temperature of the small system [34,35]. It has been shown in [34,35] that…”

“…It is also the difference between the heat transfer in a reversible process and the actual heat transfer [34,35]. In our notations, δ Q = E eq − E ex and further δS = S eq − S ex with the subscript ex for the corresponding experimental quantities in the closed system when approaching the equilibrium state.…”