Exact fluctuating hydrodynamics of active lattice gases—typical fluctuations

Abstract

We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions exactly in the homogeneous phase, we find that two macroscopic length scales develop in the system. The first is related to the diffusive length of the particles and the other to the collective behavior of the particles. The latter diverges as the critical point is approached. Our results show that the critical behavior of the model in one dimension belongs to the universality class of a mean-field Ising model, both for static and dynamic properties, when the thermodynamic limit is taken in a specified manner. The results are compared to the critical behavior exhibited by the ABC model. In particular, we find that in contrast to the ABC model the density large deviation function, at its Gaussian approximation, does not contain algebraically decaying interactions but is of a finite, macroscopic, extent which is dictated by the diverging correlation length.

Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

“…2 /2ρ close to the minimum the joint largedeviation function exactly matches the Gaussian noise term derived in Ref. [43].…”

Macroscopic fluctuation theory and current fluctuations in active lattice gases

“…In this paper, we derive a non-Gaussian MFT that fully encompasses the Poissonian noise, extending our previous work on small Gaussian fluctuations [43]. We then apply this extended MFT framework to study the distribution of the time-integrated current flowing through the system.…”

“…In Refs. [39,43] it was shown that the density fields defined in Eq. ( 1) obey the fluctuating hydrodynamic equations…”

“…On general grounds the fluctuations scale as L −1/2 at large L. In Ref. [43], we exploited an exact mapping to the well studied ABC lattice gas model [64][65][66] to derive an expression for typical small Gaussian fluctuations. Using these we were able to characterize the critical behavior of the model exactly, finding that it belongs to the mean-field Ising universality class both for static and dynamic properties.…”

“…In a previous work [43], we derived the fluctuating hydrodynamics of this model in the regime of small typical Gaussian fluctuations. This enabled us to find the static and dynamical correlation functions of the model in the homogeneous phase.…”