Statistical physics approaches in population dynamics
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We examine a multiscale framework for modeling the time evolution of size distribution densities of multiple populations. The model builds upon classical Boltzmann-type equations, where the dynamics arise from elementary interactions between individuals. This approach captures the stochastic and nonlinear nature of population-level behavior and provides a natural transition from microscopic interaction rules to macroscopic dynamics. The results establish a bridge between kinetic modeling and classical population dynamics, offering a multiscale perspective on a series of biologically relevant scenarios. Connections with mean-field limits and emergent collective behavior through new entropy inequalities will also be discussed, illustrating how tools from statistical physics can enrich our understanding of structured population models.