Entropy measurements in mesoscopic circuits: opportunities and limitations*

Recently, Hartman et al. demonstrated the capability to measure the entropy of a quantum dot (QD) containing only a few electrons^[1] by detecting shifts in the charge state of the dot with temperature, dN/dT. While the measurement technique in Hartman et al. achieved a high level of accuracy, it lacked versatility because it required the system to be in a weakly coupled state that is thermally broadened, and therefore that charge transitions have the standard cosh² line-shape of classic Coulomb blockade theory. Here, we show that integrating the dN/dT signal instead of fitting to a particular line-shape enables an entropy measurement of any transition^[2], independent of the transition line-shape or even whether the entropy change occurs in the QD itself or another part of the system that is directly coupled to the dot. We demonstrate an entropy measurement for QDs throughout the range from weak to strong coupling to a reservoir. The QD is also sensitive to changes in entropy of other parts of the system, illustrating the potential for this method to be used to measure the entropy of more complex and interesting systems.

[1] Hartman, N. et al. (2018). Nature Physics, 14(11), pp.1083-1086.
[2] Sela, E. et al. (2019). PRL, 123(14).