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Fractional entropy is a signature of nonlocal degrees of freedom, such asMajorana zero modes or more exotic non-Abelian anyons. Although directexperimental measurements remain challenging, Maxwell relations provide anindirect route to the entropy through charge measurements. Here we considermultichannel charge-Kondo systems, which are predicted to host exoticquasiparticles due to a frustration of Kondo screening at low temperatures. Inthe absence of experimental data for the charge occupation, we derive relationsconnecting the latter to the conductance, for which experimental results haverecently been obtained. Our analysis indicates that Majorana and Fibonaccianyon quasiparticles are well-developed in existing two- and three-channelcharge-Kondo devices, and that their characteristic $k_{\rm{B}}\log\sqrt{2}$and $k_{\rm{B}}\log\frac{1+\sqrt{5}}{2}$ entropies are experimentallymeasurable.

Fractional entropy of multichannel Kondo systems from conductance-charge relations