ОСОБЕННОСТИ ПРИМЕНЕНИЯ МЕТОДОВ СТАТИСТИЧЕСКОЙ МЕХАНИКИ ПРИ ИССЛЕДОВАНИИ ОБОБЩЕНИЙ КЛАССИЧЕСКОЙ ЦЕПОЧКИ ВОЛЬТЕРРА

Abstract

An analytical study of one of the generalizations of the classical Volterra chain (coupled Volterra chain) has been carried out. The use of methods and approaches of statistical mechanics in the study made it possible to identify a number of important features of such models, which are currently widely used in research in chemistry, ecology, biology, economics, hydrodynamics, astrophysics, plasma physics. The advantage of the studied model is that the introduction of additional variables makes it possible to take into account a greater number of factors influencing the dynamics of the system without changing its algebraic structure. However, an attempt at a statistical description of the model reveals a significant drawback - the partition function of the system becomes divergent. In this regard, the possibility of an adequate statistical description of the coupled Volterra chain in the case of divergence of its partition function is investigated. For the selected specific model, the sources of the divergence of the partition function are identified, and a method for their cancel out is proposed. The partition function is calculated in an explicit and finite form, which allows us to state that an adequate statistical description of the phenomena described by this model is possible. Given the wide range of applications of the coupled Volterra chain, the results obtained are of interest to theorists and practitioners when analyzing and predicting the results of a statistical study of various generalizations of the model.