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, could it result from an exchange of entropy with the macroscopic meter? This possibility is explored, presenting a model for spin measurement in a unitary setting and some preliminary analytical results based on it.
Highlights
With the advent of the first publications proposing the concept of deterministic chaos and substantiating it with a novel tool, computer simulations, more was achieved than just a major progress in fields such as weather and turbulence [1]
If there is a two-way traffic, an interchange of entropy between the system and environment, this principle, applied in turn to quantum measurement, has a tantalizing consequence: it suggests that besides decoherence, besides the collapse of the wave packet, the randomness apparent in the outcomes of quantum measurements could be traced back to the environment and could be interpreted as a manifestation of entropy interchanged with the macroscopic apparatus as a result of their entanglement during the measurement
The data shown provide clear evidence that incoherent processes induced by measurements destroy dynamical localization
Summary
With the advent of the first publications proposing the concept of deterministic chaos and substantiating it with a novel tool, computer simulations, more was achieved than just a major progress in fields such as weather and turbulence [1]. If there is a two-way traffic, an interchange of entropy between the system and environment, this principle, applied in turn to quantum measurement, has a tantalizing consequence: it suggests that besides decoherence, besides the collapse of the wave packet, the randomness apparent in the outcomes of quantum measurements could be traced back to the environment and could be interpreted as a manifestation of entropy interchanged with the macroscopic apparatus as a result of their entanglement during the measurement
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