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Compositional Thermostatics
John C. Baez, Owen Lynch, Joe Moeller
We define a thermostatic system to be a convex space of states together with a concave function sending each state to its entropy, which is an extended real number. This definition…
Getting to the Bottom of Noether's Theorem
John C. Baez
We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic app…
Open Systems in Classical Mechanics
John C. Baez, David Weisbart, Adam M. Yassine
Generalized span categories provide a framework for formalizing mathematical models of open systems in classical mechanics. We introduce categories and $\mathsf{Ha…
Coarse-Graining Open Markov Processes
John C. Baez, Kenny Courser
Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processe…
A Compositional Framework for Reaction Networks
John C. Baez, Blake S. Pollard
Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemist…
A Compositional Framework for Markov Processes
John C. Baez, Brendan Fong, Blake S. Pollard
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inpu…