ABSTRACT
Algorithmic probability is a seminal concept in the theory of algorithmic information. The concept of algorithmic information dynamics or simply algorithmic dynamics was introduced in and draws heavily on the theories of computability and algorithmic information. It has been proven that there are quantitative connections between indicators of algorithmic information content and the chaotic behaviour of dynamical systems that is related to their sensitivity to initial conditions. The purpose of algorithmic dynamics is to trace in detail the changes in algorithmic probability—estimated by local observations—produced by natural or induced perturbations in evolving open complex systems. The chapter shows how the algorithmic tools enabling the area that algorithmic information dynamics can be used in what is known already to be capable of doing better than Shannon Entropy and common compression. Lossless compression algorithms have traditionally been used to approximate the Kolmogorov complexity of an object.
