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We introduce time-dependent, generalized factorial cumulants $C_s^m(t)$ ofthe full counting statistics of electron transfer as a tool to detectinteractions in nanostructures. The violation of the sign criterion $(-1)^{m-1}C^m_s(t)\ge0$ for \emph{any} time $t$, order $m$, and parameter $s$ proves thepresence of interactions. For given system parameters, there is a minimal timespan $t_\text{min}$ and a minimal order $m$ to observe the violation of thesign criterion. We demonstrate that generalized factorial cumulants are moresensitive to interactions than ordinary ones and can detect interactions evenin regimes where ordinary factorial cumulants fail. We illustrate our findingswith the example of a quantum dot tunnel coupled to electronic reservoirseither in or out of equilibrium.

Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium