Measurements of entropy provide important information about a system’s microscopic dynamics, such as the number, degeneracy, and relative energies of electronic states; the value of spin and degree of localization and entanglement; and the emergence of exotic states.

In macroscale systems, entropy is calculated from calorimetric approaches using temperature measurements. However, in extremely small systems such as quantum dots and single molecules, thermometers are typically several orders of magnitude larger than the system. This makes measurements difficult and uncertainties large.

Pyurbeeva et al. discussed how entropy can be measured in small systems using individual electrons to explore the phase space of the system and obtaining the number and accessibility of free states from properties like mean charge and current.

The team hopes to provide a helpful introduction for those interested in the field by including the theoretical background and examples of applications.

“Macroscopically, electronic entropy measurements are emerging as a new method for studying dynamics of nanoscale objects — a very common problem both in fundamental condensed matter physics and for practical applications, such as molecular electronics,” said author Eugenia Pyurbeeva. “Microscopically, we would like to stress that one has to be very careful when extending thermodynamics to small systems.”

The researchers aim to apply these entropy measurements to study the impact of spin-entropy on the efficiency of molecular heat engines. They are also interested in using thermodynamic properties to examine the behavior of nanodevices under a wider range of conditions than have been explored previously.

Source: “Electronic measurements of entropy in meso- and nanoscale systems,” by Eugenia Pyurbeeva, Jan A. Mol, and Pascal Gehring, Chemical Physics Reviews (2022). The article can be accessed at