The Second-Class Particle in the Half-Line Open Totally Asymmetric Simple Exclusion Process.

We consider the second-class particle in half-line open totally asymmetric exclusion process (TASEP) under two different initial conditions with shock discontinuities. The exact formulas for the distribution of the second-class particle can be derived by using the color-position symmetry theorem of colored half-space TASEP. We study the asymptotic distributions of second-class particles under the constant scaling and Kardar-Parisi-Zhang-type scaling.