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

Abstract

Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue that quantum chaos came as an indispensable rectification, removing inconsistencies related to entropy in classical chaos: Bottom-up information currents require an inexhaustible entropy production and a diverging information density in phase space, reminiscent of Gibbs' paradox in Statistical Mechanics. It is shown how a mere discretization of the state space of classical models already entails phenomena similar to hallmarks of quantum chaos, and how the unitary time evolution in a closed system directly implies the ''quantum death'' of classical chaos. As complementary evidence, I discuss quantum chaos under continuous measurement. Here, the two-way exchange of information with a macroscopic apparatus opens an inexhaustible source of entropy and lifts the limitations implied by unitary quantum dynamics in closed systems. The infiltration of fresh entropy restores permanent chaotic dynamics in observed quantum systems. Could other instances of stochasticity in quantum mechanics be interpreted in a similar guise? Where observed quantum systems generate randomness, that is, produce entropy without discernible source, could it have infiltrated from the macroscopic meter? This speculation is worked out for the case of spin measurement.

arXiv comment41 pages, 17 figures

References in corpus (12)

• Decoherence, einselection, and the quantum origins of the classical
• Decoherence, Chaos, and the Second Law
• Long-Time Correlations in the Stochastic Regime
• Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator
• Gaussian Decoherence from Random Spin Environments
• Decoherence from spin environments
• Objective properties from subjective quantum states: Environment as a witness
• Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
• Semi-classical and quantum Rabi models: in celebration of 80 years
• Ehrenfest times for classically chaotic systems
• Classical small systems coupled to finite baths
• Quantum dynamical entropy and decoherence rate

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