  We introduce and study a model of hardcore particles obeying run-and-tumble
dynamics on a one-dimensional lattice, where particles run in either +ve or -ve
$x$-direction with an effective speed $v$ and tumble (change their direction of
motion) with a constant rate $\omega.$ We show that the coarse-grained dynamics
of the system can be mapped to a beads-in-urn model called misanthrope process
where particles are identified as urns and vacancies as beads that hop to a
neighbouring urn situated in the direction opposite to the current. The hop
rate, same as the magnitude of the current, depends on the total number of
beads present in the departure and the arrival urn; we calculate it
analytically and show that it does not satisfy the criteria required for a
phase separation transition. Tumbling is generally detrimental to the stability
of jamming; thus, our results for this restricted tumbling model strongly
suggest that motility induced phase separation transition can not occur in one
dimension.
