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Quantum chaos is presented as a paradigm of information processing bydynamical systems at the bottom of the range of phase-space scales. Startingwith a brief review of classical chaos as entropy flow from micro- tomacro-scales, I argue that quantum chaos came as an indispensablerectification, removing inconsistencies related to entropy in classical chaos:Bottom-up information currents require an inexhaustible entropy production anda diverging information density in phase space, reminiscent of Gibbs' paradoxin Statistical Mechanics. It is shown how a mere discretization of the statespace of classical models already entails phenomena similar to hallmarks ofquantum chaos, and how the unitary time evolution in a closed system directlyimplies the ''quantum death'' of classical chaos. As complementary evidence, Idiscuss quantum chaos under continuous measurement. Here, the two-way exchangeof information with a macroscopic apparatus opens an inexhaustible source ofentropy and lifts the limitations implied by unitary quantum dynamics in closedsystems. The infiltration of fresh entropy restores permanent chaotic dynamicsin observed quantum systems. Could other instances of stochasticity in quantummechanics be interpreted in a similar guise? Where observed quantum systemsgenerate randomness, that is, produce entropy without discernible source, couldit have infiltrated from the macroscopic meter? This speculation is worked outfor the case of spin measurement.

Quantum Chaos and Quantum Randomness - Paradigms of Entropy Production on the Smallest Scales