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Explore quantum bounds for transport coefficients and their connection to the Fluctuation-Dissipation Relation in this 39-minute conference talk by Jorge Kurchan. Delve into the intriguing world of quantum physics as Kurchan discusses conjectured bounds for viscosity and conductivity, their significance in high-energy physics, and their relation to String Theory and Black Holes. Learn about the proven bound for the quantum Lyapunov exponent and understand how the Maldacena-Shenker-Stanford argument can be simplified to reveal its connection to the quantum Fluctuation-Dissipation (KMS) relation. Gain insights into potential approaches for addressing transport cases and expand your knowledge of quantum physics and its applications in various fields. This talk was presented as part of the Thematic Programme on "Large Deviations, Extremes and Anomalous Transport in Non-equilibrium Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics.