# Out-of-time-order fluctuation-dissipation theorem. (arXiv:1612.08781v4 [cond-mat.stat-mech] UPDATED)

We prove a generalized fluctuation-dissipation theorem for a certain class of
out-of-time-ordered correlators (OTOCs) with a modified statistical average,
which we call bipartite OTOCs, for general quantum systems in thermal
equilibrium. The difference between the bipartite and physical OTOCs defined by
the usual statistical average is quantified by a measure of quantum
fluctuations known as the Wigner-Yanase skew information. Within this
difference, the theorem describes a universal relation between chaotic behavior
in quantum systems and a nonlinear-response function that involves a
time-reversed process. We show that the theorem can be generalized to
higher-order $n$-partite OTOCs as well as in the form of generalized
covariance.