On the distribution of a second-class particle in the asymmetric simple exclusion process

Imagine that the particles in the system are each called either first class or second class. The evolution is the same as before, except that if a second-class particle attempts to go to a site occupied by a first-class particle, it is not allowed to do so, while if a first-class particle attempts to move to a site occupied by a second-class particle, the two particles exchange positions. In other words, a first-class particle has priority over a second-class particle. This rule has no effect on whether or not a given site is occupied at a given time. The advantage, though, is that viewed by itself, the collection of first-class particles is Markovian, and has the same law as the exclusion process. The collection of second-class particles is clearly not Markovian. However, the collection of firstand second-class particles is Markovian, and again evolves like an exclusion process.