Controlling the Entropy of a Single-Molecule Junction

The statistical interpretation of entropy first given by Boltzmann connects entropy as a thermodynamic state function to the number of microstates available to the system. Yet, this connection is generally not quantifiable for macroscopic systems, containing Avogadro’s numbers (~10²³)of molecules, which have too many configurations to be tractable. For mesopic and nanoscopic few-electron systems with tractable electron and spin configurations this connection is genrally not quantifiable either, as standard experimental ways of measuring entropy through heat capacity cannot be applied as they require the measurement of immeasurable small amounts of heat. To overcome this conundrum and reveal the relation between entropy and correlations in few-electron quantum systems, we have developed a self-consistent thermodynamic framework which connects macroscopic observable quantities, including electrical current and charge, to microscopic configuration entropy in the form of spin-degeneracy. We apply this thermodynamic framework and use thermoelectric conductance spectroscopy to directly measure the entropy of a single nitronyl nitroxide free radical single-molecule quantum device. Our entropy measurements indicate that the neutral molecule holds an unpaired electron and is therefore in a doublet ground state, while the ground state of the reduced molecule is a singlet with all electrons paired. By applying a magnetic field, a low-lying triplet excited state is revealed which was not observed in conventional charge transport measurements. The ability to directly measure entropy of individual molecules without the need of a priori knowledge of its electronic structure has the potential to provide insights into their nontrivial quantum states, such as high-spin ground states, Kondo states, Majorana modes, and nonabelian anyons, and shed light on the discriminating role of entropy in driving electron transfer rates.