Generalized TASEP on open chains with a modified injection condition

TL;DR

This paper introduces a new version of the generalized TASEP on open chains with a modified injection condition, incorporating additional particle interactions and analyzing its analytical solvability and differences from previous models.

Contribution

It presents a novel gTASEP model with modified boundary conditions and additional particle interactions, expanding the understanding of exclusion processes.

Findings

Analytically solvable version of gTASEP with modified injection boundary.

Comparison with previous gTASEP models on open tracks.

Preliminary results indicating new interaction effects.

Abstract

We report here our preliminary results in the study of a new version of the generalized Totally Asymmetric Simple Exclusion process (gTASEP) on open tracks. In the gTASEP an additional interaction between the particles is considered, besides the hard-core exclusion, which exists in the standard TASEP. It is modeled by the introduction of a second hopping probability $p_m$ for the particles, belonging to the same cluster, in addition to the standard hopping probability p, which now applies only for single particles and the head (rightmost) particle of a cluster. We briefly describe how one can obtain analytically solvable version of gTASEP by modifying the left (injection) boundary condition. A short comparison is made with the previously studied version of gTASEP on open tracks.