Quantum bounds and Fluctuation-Dissipation Relation

Quantum bounds for transport coefficients - viscosity, conductivity - have been conjectured for some time. They have attracted strong interest because models associated with holography and black holes are expected to saturate them. Also, very importantly, because they could explain the similarity in transport coefficients of apparently dissimilar systems. 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.