First and Second Law of Thermodynamics Constraints in the Lifshitz Theory of Dispersion Forces

The presence of dominant interatomic dispersion forces on the nanoscale holds the promise for breakthrough applications in key areas of quantum sensing, such as accelerometry, as well as nano-manipulation and energy storage. In order to do work, nano-machines enabled by dispersion forces must exchange energy with the surrounding environment. Such processes can be described in terms of thermodynamical engine cycles involving individual atoms or material boundaries, separated by possibly empty gaps and interacting via time-dependent dispersion forces. The fundamental strategy indispensable to achieve dispersion force time-modulation, demonstrated experimentally by independent groups on different scales, is based on the illumination of interacting, semiconducting elements by appropriate radiation beams. Here we analyze the operation of ideal nano-engines in the quasi-static regime by means of the Lifshitz theory of dispersion forces involving semiconducting boundary or atom irradiation. Firstly, we verify that the First Law of Thermodynamics is satisfied so that the total energy of the system is rigorously conserved. Secondly, we show that, within this first approximate treatment, the Second Law of Thermodynamics may be violated for extremely small interboundary gap widths. We identify important limitations to be addressed to determine whether this is a reliable conclusion. The technological and historic backdrops are presented, and important topics for future research are identified.