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Is there any classical model which deals with the birth, life and death of particles? What application could it have?

I am talking about a 'billiard-ball' kind of model, but the kind in which balls keep popping in and out.

What would the configuration space of such a system be like if particle number was not conserved? How would the Hamiltonian evolve with time?

I am not interested in a statistical models.

I can't think of any real world application of such a model. But perhaps there is a mathematical apparatus to deal with the continuous evolution of such systems?

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  • $\begingroup$ Is the popping in and out random, or deterministic? Conway's game of life might be an example. The billiard balls could be gliders. $\endgroup$
    – user4552
    Sep 7, 2013 at 16:12
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    $\begingroup$ Roughly speaking, the Hamiltonian formalism talks about energy, and the reason we care about energy is that it's conserved. If objects pop up out of nowhere, it seems like energy isn't going to be conserved. Or were you thinking of collisions sort of like vertices of Feynman diagrams...? $\endgroup$
    – user4552
    Sep 7, 2013 at 16:45
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    $\begingroup$ The Boltzmann equation is about the distribution of particles in phase space. It allows for different kinds of particles that change from one form into another, which implies particle creation and destruction. It has applications in plasma physics. $\endgroup$
    – auxsvr
    Jul 8, 2015 at 22:18

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