Starting from a simple example of independent particles, we discuss the evolution of (well-chosen) product measures, and show that there is an intertwined evolution on the parameters of these product measures (so-called hidden parameter model). We extend this intertwining to several interacting systems. In some examples, the intertwined dynamics is “exactly solvable” due to a Markov structure in space. In these cases, one can find explicit formulas for the “non-equilibrium steady state”.

Based on joint works with C. Giardinà (Modena) and B. van Tol (Delft).