Mapping current and activity fluctuations in exclusion processes: consequences and open questions

Considering the large deviations of activity and current in Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between joint scaled cumulant generating functions two ASEPs with different parameters. This mapping is obtained by applying similarity transform on deformed Markov matrix source model order to obtain target model. We first derive this for periodic boundary conditions, diffusive scaling limit (corresponding Weakly Processes, or WASEP) how expressed language Macroscopic Fluctuation Theory (MFT). As an interesting specific case, map ASEP SSEP, thereby uncovering regime Kardar--Parisi--Zhang distribution SSEP. At activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114, 060601 (2015)]. Using results from quantum spin chain theory, characterize hyperuniform evaluating small wavenumber asymptotic behavior structure factor at half-filling. Conversely, formulate MFT conjecture correlation function chains any fixed total magnetization (in thermodynamic limit). In addition, generalize case open reservoirs, apply it WASEP formalism. also allows us find symmetry-breaking dynamical phase transition (DPT) conditioned prior knowledge DPT current.