Are chaotic systems dynamically random?

Abstract

Physical systems can be characterized by several types of complexity measures which indicate the computational resources employed. With respect to these measures, several chaos classes may be distinguished. There exists a constructive approach to random physical motion which operates with computable initial values and deterministic evolution laws. For certain limits, these chaos classes render identical forms of random physical motion. These observations may have some implications on a unique time direction for macroscopic reversible systems.

The quantum coin toss-testing microphysical undecidability

“…There is no space here to discuss different definitions of randomness, such as normalized randomness, i.e., K(x(n)) ≡ lim n→∞ H(x(n))/n > 0, which has important applications in symbolic dynamics[17,6], or definitions of randomness based upon complexity measures[18,16,19].…”

On the Computational Power of Physical Systems, Undecidability, the Consistency of Phenomena, and the Practical Uses of Paradoxes

“…A similar treatment of the halting problem [34] for a quantum computer leads to the conclusion that the quantum recursion theoretic "solution" of the halting problem reduces to the tossing of a fair (quantum [42]) coin [43]. Another, less abstract, application for quantum information theory is the handling of inconsistent information in databases.…”