A Criterion for the Persistence of Dissipative Structures and an Operational Method for Its Evaluation

Preprint — not peer reviewed. This study proposes a criterion for the persistence of dissipative structures in terms of information continuity between time points retained under relevant environmental conditions, together with an operational method for its evaluation. As a proof of concept, time-series images of a Belousov-Zhabotinsky (BZ) reaction were analyzed using normalized mutual information (NMI) and image change between local image patches at different time points. A passive Gaussian linear-diffusion reference was constructed from the processed initial image of each frame pair. When image-change magnitude was approximately matched, the BZ image series retained higher NMI than the Gaussian reference under the conditions examined. The experiment does not directly estimate the conditional mutual information used in the theoretical persistence criterion. Rather, it provides a proof of concept for an observable image-based approximation of information dependence between time points in a changing dissipative structure. This Zenodo record contains two corresponding versions of the manuscript: English version: A Criterion for the Persistence of Dissipative Structures and an Operational Method for Its Evaluation Japanese version: 散逸構造の持続判定条件とその操作的方法 The English manuscript is the primary version. The Japanese manuscript is provided as a corresponding Japanese-language version. This work builds on the theoretical framework introduced in: Sugizono, Y. (2026). Persistence as Recursive History Formation: A Conditional-Information Framework under Diffusive Conditions. Zenodo. https://doi.org/10.5281/zenodo.20102251