John Baez

Dynamics, Thermodynamics and Information Processing in Chemical Networks

June 13, 2017

The Mathematics of Open Reaction Networks

To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, electrical circuit diagrams, signal-flow graphs, Feynman diagrams and the like. In principle all these different diagrams fit into a common framework: the mathematics of monoidal categories. This has been known for some time. However, the details are more challenging, and ultimately more rewarding, than this basic insight. Here we explain how various applications of reaction networks and Petri nets fit into this framework.

You can see the slides here.

After I gave my talk, Blake Pollard gave a closely related talk:

Black-boxing open reaction networks

An open reaction network is a reaction network that interacts with its environment, a user, or another system. I'll describe a way to treat open reaction networks as morphisms in a category. Composition in this category provides a means of building up larger open reaction networks from smaller ones. For reaction networks obeying mass action kinetics, I'll describe a functor sending an open reaction network to the relation between input and output flows that holds in nonequilibrium steady states. This provides a compositional approach to studying nonequilibrium steady states.

You can see Blake Pollard's slides here.

There are lots of links to papers in the slides, especially near the end. To read more about the network theory project, go here:

For a video of a related talk assuming more knowledge of category theory, try this:

© 2017 John Baez