Table 1. A recipe-book for constructing Hamiltonians from transition rates.

	Transition	Contribution to H
One-body terms	diffusion of a, rate κ
	death of a, rate μ
	change (b→c), rate ν
Two-body terms	competition, kernel V
	infection,(a→b)
	birth, dispersal kernel V

One-body terms are integrated over x and two-body terms are integrated over both x and y. The positive terms correspond to the efflux of probability from a configuration state, and the negative terms effect the flow of probability into a new state.