A bound on chaos

Juan Maldacena, Stephen H. Shenker, Douglas Stanford

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum
systems with a large number of degrees of freedom. Chaos can be diagnosed using
an out-of-time-order correlation function closely related to the commutator of
operators separated in time. We conjecture that the influence of chaos on this
correlator can develop no faster than exponentially, with Lyapunov exponent
$\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument,
based on plausible physical assumptions, establishing this conjecture.