  The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the
scrambling of quantum information via the spread of entanglement. The OTOC
encodes forward and reverse evolutions and has deep connections with the flow
of time. So do fluctuation relations such as Jarzynski's Equality, derived in
nonequilibrium statistical mechanics. I unite these two powerful, seemingly
disparate tools by deriving a Jarzynski-like equality for the OTOC. The
equality's left-hand side equals the OTOC. The right-hand side suggests a
protocol for measuring the OTOC indirectly. The protocol is
platform-nonspecific and can be performed with weak measurement or with
interference. Time evolution need not be reversed in any interference trial.
The equality opens holography, condensed matter, and quantum information to new
insights from fluctuation relations and vice versa.
