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

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.