  We propose a method of estimating ergodization time of a chaotic
many-particle system by monitoring equilibrium noise before and after time
reversal of dynamics (Loschmidt echo). The ergodization time is defined as the
characteristic time required to extract the largest Lyapunov exponent from a
system's dynamics. We validate the method by numerical simulation of an array
of coupled Bose-Einstein condensates in the regime describable by the discrete
Gross-Pitaevskii equation. The quantity of interest for the method is a
counterpart of out-of-time-order correlators (OTOCs) in the quantum regime.
