Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

Abstract

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.

Entropy production and its large deviations in an active lattice gas

“…As was argued before [13,22], when the system approaches MIPS criticality, the onset of the transition to the smoothly modulated phase happens at vanishingly small IEPR bias, so that the bias-induced and motilityinduced instabilities merge. A similar phenomena was reported in the study of current fluctuations in [30].…”

“…We now describe the fluctuating hydrodynamics of this model, as derived in [29,30]. For passive lattice gasses, such a description was widely employed in the context of the macroscopic fluctuation theory (MFT), see [39] for a review.…”

“…The same biasing strategy can of course be used to look at large deviations of other physical quantities such as currents. (This is done for the specific model explored below in [29,30]. )…”

“…For this active lattice gas model, the noiseless coarse-grained hydrodynamics was established first in [38]. Later, in [29,30] this was complemented with an exact large deviation framework for macroscopic fluctuations. (We rely heavily on this framework below.)…”

Interacting, running and tumbling: The active Dyson Brownian motion

“…have been developed [2,20,28,29]. At present, very few exact results exist, even in one dimension, beyond two interacting RTP's on the line [19,[30][31][32][33][34][35], and harmonic chains [36,37].…”