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The Sachdev-Ye-Kitaev (SYK) model describes electrons with random andall-to-all interactions, and realizes a many-body state without quasiparticleexcitations, and a non-vanishing extensive entropy $S_0$ in the zerotemperature limit. Its low energy theory coincides the low energy theory of thenear-extremal charged black holes with Bekenstein-Hawking entropy $S_0$.Several mesoscopic experimental configurations realizing SYK quantum dynamicsover a significant intermediate temperature scale have been proposed. Weinvestigate quantum thermoelectric transport in such configurations, anddescribe the low temperature crossovers out of SYK criticality into regimeswith either Fermi liquid behavior, a Coulomb blockade, or criticalityassociated with Schwarzian quantum gravity fluctuations. Our results show thatthermopower measurements can serve as a direct probe for $S_0$.

Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments