At time zero, there are N identical point particles in 1D characterized by their positions and velocities. Both quantities are given randomly and independently from each other, with arbitrary probability densities. Each particle evolves at constant velocity until eventually they meet. When this happens, a perfectly-plastic collision is produced, resulting in a new particle composed by the sum of their masses and the weighted average velocity. Merged particles evolve indistinguishably from the non-merged ones. Particles are not confined to any region or reservoir, so as time progresses, they go on to infinity. From this non-equilibrium process, we ask if at time zero, just from the initial conditions (without evolving the system): (A) Can the exact number of final particles be determined? (B) What is the average number of final particles? (C) What is the mass distribution of these final particles? (D) How much energy is lost?
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