Algorithmic complexity and randomness in elastic solids

TL;DR

This paper investigates how elastic solids transform the randomness of external forces based on their algorithmic complexity, demonstrating that more complex systems produce less random output sequences.

Contribution

It introduces a numerical analysis framework linking the complexity of elastic solids to their effect on input randomness, supporting the theory that physical systems act as algorithmic selection rules.

Findings

Higher system complexity leads to less random output sequences.

The system's complexity can be controlled via external parameters.

Results support the theory that physical systems behave as algorithmic selection-rules.

Abstract

A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input force sequence in a way proportional to its algorithmic complexity. We demonstrate this by numerical analysis of a one-dimensional vibrating elastic solid (the system) on which we apply a maximally random input force. The level of complexity of the system is controlled via external parameters. The output response is the field of displacements observed at several positions on the body. The algorithmic complexity and stochasticity of the resulting output displacement sequence is measured and compared against the complexity of the system. The results show that the higher the system complexity the more random-deficient the output sequence. This agrees with the theory introduced in [16] which states that physical systems such as this behave as algorithmic selection-rules which act on random actions in their surroundings.