  We investigate why the Lyapunov exponents $\lambda$ of out-of-time-ordered
correlators (OTOCs) satisfy a universal bound $\lambda < 2 \pi k_B T/{\hbar}$
by probing imaginary-time path-integral space using ring-polymer molecular
dynamics (RPMD) for a barrier-crossing model. We find that the RPMD OTOC
satisfies the same bound as the quantum OTOC, which is caused by the stability
of quantum thermal fluctuations around the instanton on the barrier. We expect
that similar instantons (or other delocalised structures) will be found in many
other systems with exponentially growing OTOCs.
