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Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems

by Mauricio J. del Razo and Luigi Delle Site

Submission summary

Authors (as registered SciPost users):

Mauricio del Razo

Abstract

A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology; ranging from the exchange of energy and matter with the surrounding environment to the change of particle numbers through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we discuss complementary physico-mathematical approaches of varying numbers of particles inspired by different specific numerical goals. Based on the underlying structure of these models, we formulate a unifying master equation for general dynamical systems with varying numbers of particles. This equation not only embeds all the previous models but enables modeling a much larger range of complex systems ranging from molecular to social agent-based dynamics.

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• Provide a novel and synergetic link between different research areas.
• Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
• Detail a groundbreaking theoretical/experimental/computational discovery
• Present a breakthrough on a previously-identified and long-standing research stumbling block