Structure coarsening, entropy and compressed space dimension

This paper outlines a new compression algebra formalism for analysing the relations between entropy, negentropy and data reduction, where reduction is described as a dimension (D) of a subspace in the initial system. First used to analyse a random system with different states, this formalism showed that there exists an isomorphism between the system entropy and its dimension (D) that becomes a random value. Applied to a physical system, we show that D well characterises the diffusion rate law of coarsening processes and particularly the different stages of diffusion with respect to time, i.e. a linear relation in liquid–solid phase, a power law in solid–solid diffusion and a constant value at equilibrium. A relation between D and the fractal dimension is shown on a grain with self-similar fractal structure submitted to a diffusion process. D could be an efficient parameter to quantify the influence of a variable in the dynamics of a physical system and it is particularly helpful in the research of invariant parameters.