Scale-Free Patterns by Synchronous Word Connectivity Sustainably for Chronological Variation

The evolution of natural language is characterized by the incorporation of a dependency structure into word sequences. Scale-free pattern regularity, in which the frequency of words conforms to a common pattern based on their rank in a list, is empirically well-known. As statistical regularity has been observed in natural and social phenomena, understanding its standard principle is of great significance. To yield a scale-free rank-size relation, procedures have been established for distributing resources such as words to elements based on the rich-get-richer mechanism. However, such procedures do not address the relevance of the dependency among elements. Using a scheme that considers the occurrence of a word as the task of assigning an energy particle to an element in a dissipative system, I implemented a computational system to select synchronously connected elements in conjunction with a model of the noise-induced synchronization phenomenon. I empirically demonstrated that the energy particle distribution for spatio-chronological freedom could provide a scale-free rank-size relation to reach a steady state of dynamic equilibrium corresponding to the most probable case in the system. Furthermore, I observed an interference fringe-like pattern in the scale-free energy particle distribution that self-organized into a stationary wave through the superposition of a wave function for energy particle assignments. The results obtained by the computational system demonstrate that statistical regularity can be provided by dependency relations with chronological variation sustainability, paving the way for the development of a methodology for evolutionary language modeling.