On the integrability of the deformed Rule 54 model

I will discuss the integrability property of a stochastic and quantum deformation of the Rule 54 cellular automaton: the simplest microscopic (deterministic) reversible model in 1+1 discrete space and time dimensions with strong local interactions. First, I will introduce the Rule 54 model and its two deformations: In the stochastic case, I couple the system to stochastic boundary reservoirs and show that the resulting non-equilibrium steady states can be constructed explicitly in matrix product form. In the quantum case, I explain how the model can be embedded into the Yang-Baxter integrability framework. It turns out that Yang- Baxter integrability is more common than previously thought! Based on ongoing work with T. Prosen.