Quantifiying spatial structure in dynamical systems: from microscopic reversibility to macroscopic irreverersibility

Two information-theoretic frameworks developed for quantifying spatial structure in dynamical systems are reviewed. In the case of microscopic dynamics, the formalism is applied to cellular automata. Even though entropy is conserved when the dynamics is reversible, there are examples in which the “complexity” of the system increases in time resulting in an apparently more random situation. In the case of macroscopic dynamics, we present a set of quantities that can be used for characterising flows of information in the process of pattern formation in spatially extended chemical dynamics. The connection between these concepts and thermodynamics is discussed.