AbstractWe obtain a new relation between the distributions $$\upmu _t$$
μ
t
at different times $$t\ge 0$$
t
≥
0
of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$
μ
t
backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$
μ
t
which in turn brings new identities for expectations with respect to $$\upmu _t$$
μ
t
. The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.
A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
