Universality classes in out-of-equilibrium systems: An encompassing theorem for a one-dimensional fusing particles model

This paper supports the idea that some out-of-equilibrium systems can be described by universality classes. A specific out-of-equilibrium fusing particles model is studied in detail, resulting in a method for determining the number and mass of the final particles based solely on the initial conditions, eliminating the need to evolve the particle system. This method reveals the basis for a universality class encompassing theorem, which is developed to define other models within the same universality class. This result establishes an infinite number of models with the same behavior and scaling, two of which are described in detail.