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

## TL;DR

This paper explores how quantum chaos serves as a fundamental paradigm for entropy production at microscopic scales, highlighting differences from classical chaos and examining the role of measurement in generating quantum randomness.

## Contribution

It introduces a quantum chaos framework that rectifies classical entropy inconsistencies and discusses how measurement-induced entropy sustains chaos in quantum systems.

## Key findings

- Discretization of classical models mimics quantum chaos features.
- Unitary evolution leads to the 'quantum death' of classical chaos.
- Measurement introduces entropy, restoring chaos in quantum systems.

## 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.