We obtain a new relation between the distributions \(\upmu _t\) at different times \(t\ge 0\) 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 \(\upmu _t\) 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 \(\upmu _t\) which in turn brings new identities for expectations with respect to \(\upmu _t\). 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.

我们获得了从步骤初始配置开始的连续时间完全非对称简单排除过程（TASEP）在不同时间\(t\ge 0\)的分布\(\upmu _t\)之间的新关系。也就是说，我们提出了一个具有局部相互作用和粒子相关速率的连续时间马尔可夫过程，它在时间上向后映射 TASEP 分布\(\upmu _t\)。在向后过程下，粒子向左跳跃，动力学可以看作是离散空间哈默斯利过程的一个版本。结合前向 TASEP 演化，这导致了一个平稳的马尔可夫动力学保留\(\upmu _t\)，这反过来又为关于\(\upmu _t\) 的期望带来了新的恒等式. 反向动力学的构建基于马尔可夫图交换 Schur 过程的参数，并由 Yang-Baxter 方程的双射性激发。我们还提出了一些由我们的结构产生的推论、扩展和开放性问题。