Extracting fractional entropy of exotic quasiparticles from conductance measurements

Fractional entropy is a signature of nonlocal degrees of freedom, such as Majorana zero modes or more exotic non-Abelian anyons. However, in the mesoscopic quantum systems hosting these states direct entropy measurements remain highly challenging. One promising approach utilizes Maxwell relations to extract entropy changes from charge measurements. In this talk, applying this approach to a metallic quantum dot system, we propose a feasible way to detect the fractional entropy in the two- and three-channel Kondo effects, corresponding to Majorana and Fibonacci zero modes, respectively, by measuring the charge occupation of the dot. Furthermore, we analyze the relation between the charge occupation and the conductance, which is already measured. The entropy extracted from the experimental data strongly supports the feasility of the proposed experiment. Our protocol provides a general route towards a direct extraction of entropy from charge measurements in mesoscopic systems.