Relation between the ASEP/TASEP time variable and dual string or gravity dynamics

Determine the physical meaning of the non-stationary time variable in ASEP/TASEP within the DSSYK and dual-gravity descriptions, including whether non-stationary ASEP solutions admit a natural interpretation in the discretized string framework.

Background

The paper identifies the spatial coordinate of the ASEP steady state with Euclidean time in DSSYK and dual gravity, but the dynamical time appearing in the Markov evolution has a different role. The authors relate this evolution to rearrangements of words formed from the ASEP generators and speculate that it may represent RG operator mixing.

The unresolved issue is whether this non-stationary stochastic evolution has a natural realization on the dual string or gravity side, rather than only an analogy at the level of stationary states and transfer matrices.

References

The interpretation of stationary states of XXZ in terms of the discretized classical string in the curved space raises the question whether the non-stationary solutions to ASEP are natural in the stringy setup as well. In other words, what is the meaning of "time" in ASEP/TASEP dynamics in the dual DSSYK and gravity side?

— DSSYK, open ASEP/TASEP and 2d dilaton gravity at strong coupling  (2610.01790 - Gorsky et al., 1 Oct 2026) in Section 4, subsection “Towards the stringy (polymer) picture and RG interpretation”