Tal Agranov, Sunghan Ro, Yariv Kafri, Vivien Lecomte
SciPost Phys. 14, 045 (2023) ·
published 22 March 2023
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We study the current large deviations for a lattice model of interacting active particles displaying a motility-induced phase separation (MIPS). To do this, we first derive the exact fluctuating hydrodynamics of the model in the large system limit. On top of the usual Gaussian noise terms the theory also presents Poissonian noise terms, that we fully account for.
We find a dynamical phase transition between flat density profiles and sharply phase-separated traveling waves, and we derive the associated phase diagram together with the large deviation function for all phases, including the one displaying MIPS. We show how the results can be obtained using methods similar to those of equilibrium phase separation,
in spite of the nonequilibrium nature of the problem.
Matthieu Vanicat, Eric Bertin, Vivien Lecomte, Eric Ragoucy
SciPost Phys. 10, 028 (2021) ·
published 5 February 2021
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Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar–Parisi–Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.
