From Processes to ODEs by Chemistry

We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Chemical Parametric Form, or CPF) can be converted to chemical reactions. CPF is a subset of π-calculus, but is already more powerful that what is strictly needed to represent chemistry: it supports also parameterization and compositional reuse of models. The mapping of CPF to chemistry thus induces a parametric and compositional mapping of CPF to differential equations; the indirect mapping through chemistry is easier to define and understand than a direct mapping. As an example, we derive a quantitative interleaving law from the differential equations.