Quantum bounds for transport coefficients - viscosity, conductivity - have been conjectured

for some time. They have attracted  strong interest of high-enegy physicists

because models associated with String Theory and Black Holes are expected to saturate them.

At this time, the only such bound for which we have a proof applies to the quantum Lyapunov exponent.

The argument, developed by Maldacena, Shenker and Stanford, may be recast in a simple form that makes

it clear that the bound is a consequence of the quantum  Fluctuation -Dissipation (KMS) relation.

This perspective may perhaps give us a lead on how to proceed with the transport case.