Diffusion Without Constraints

Abstract

The consideration of developing open systems, which show structure formation like the temporal development of bubble size distribution during foam decay leads us to a new approach to diffusion processes. In this context, we refer to our articles The Apollonian Decay of Beer Foam – Bubble Size Distribution and the Lattices of Young Diagrams and their Correlated Mixing Functions (S. Sauerbrei E.C. Haß, P.J. Plath, Discrete Dynamics in Nature and Society submitted and accepted) and On the Characterization of Foam Decay with Diagram Lattices and Majorization (S. Sauerbrei U. Sydow, P.J. Plath Zeitschrift für Naturforschung A, Submitted). By the join of partition diagrams and their permutations a structure is derived, which realizes all possible distributions. Transitions containing negative probabilities become possible and the intrasystem Shannon entropy shows an oscillating behaviour. Our partition-permutation-structure enables a description of positive and negative diffusion processes – or of diffusion processes without constraints. The characteristics of the partition-permutation-structure are comparable to the properties of our foam decay.