these models is their integrability: the Markov matrix $M$ ruling their stochastic dynamics is part of a family of commuting operators generated by a transfer matrix. The transfer matrix is constructed from a $R$-matrix satisfying the Yang-Baxter equation [@Baxter]. It is well known that continuous time Markov matrices with local stochastic rules can be obtained by taking the first logarithmic derivative of an appropriate transfer matrix. This mechanism is quite general and relies only on minor assumptions on the $R$-matrix (essentially the regularity property). It has also been observed that the transfer matrix of the six vertex model can be used to define specific discrete time exclusion process [@KandelDN; @Schutz2; @SchutzS]. However we are lacking a general picture to construct discrete time Markovian dynamics from the transfer matrix, without specific assumptions on the $R$-matrix of the model.

We try to address this question in this paper by proposing a generic formalism to obtain Markovian discrete time dynamics from the transfer matrix of an integrable system. The dynamics can be written easily in terms of local Markovian operators acting on two sites of the lattice. It can be interpreted as two-step discrete Floquet dynamics, where one pair of sites over two 