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We discuss our recent study of local quantum mechanical uncertainty relationsin quantum many body systems. These lead to fundamental bounds for quantitiessuch as the speed, acceleration, relaxation times, spatial gradients and theLyapunov exponents. We additionally obtain bounds on various transportcoefficients like the viscosity, the diffusion constant, and the thermalconductivity. Some of these bounds are related to earlier conjectures, such asthe bound on chaos by Maldacena, Shenker and Stanford while others are new. Ourapproach is a direct way of obtaining exact bounds in fairly general settings.We employ uncertainty relations for local quantities from which we strip offirrelevant terms as much as possible, thereby removing non-local terms. Togauge the utility of our bounds, we briefly compare their numerical values withtypical values available from experimental data. In various cases, approximatesimplified variants of the bounds that we obtain can become fairly tight, i.e.,comparable to experimental values. These considerations lead to a minimal timefor thermal equilibrium to be achieved. Building on a conjectured relationbetween quantum measurements and equilibration, our bounds, far morespeculatively, suggest a minimal time scale for measurements to stabilize toequilibrium values.

Quantum equilibration and measurements -- bounds on speeds, Lyapunov  exponents, and transport coefficients obtained from the uncertainty relations  and their comparison with experimental data