Persistent exclusion process: comparative study of mean-field methods and possible generalizations of the model

The Persistent exclusion process(PEP) is a model for active matter that has generated some interest thanks to the fact that is able to describe the birth of clusters observed in some biological phenomena where self-propelled cells move in crowded environment, this despite the absence of any long ranged interaction included in the model. Some early studies have suggested the possibility that this model could include some sort of phase transition induced by mobility but lately it has been shown that such thing is not possible in 1 dimensional systems while for higher dimensionalities this possibility has not been explored. The present work explores the possibility to connect the 1 dimensional PEP to the family of other exclusion processes, in particular how it connects to the asymmetric exclusion processes(ASEP). In order to do that a generalized model was developed and explored where the particles of the ASEP have the possibility to enter and exit from a state where they move with a different velocity and direction with respect to the other particles. In doing that the pair approximations was tested on the PEP since it has shown remarkable successes in the description of the generalizations of the ASEP, but unfortunately it falls short against the more successful approximations developed expressly for this model.