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.

17 pages, 6 figures

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• Inclusions, Boundaries and Disorder in Scalar Active Matter
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• Thermodynamically consistent flocking: From discontinuous to continuous transitions
• Tricritical behavior in dynamical phase transitions
• Current fluctuations in an interacting active lattice gas
• Generalized disorder averages and current fluctuations in run and tumble particles
• Active Random Walks in One and Two Dimensions
• Nonequilibrium steady state of trapped active particles
• Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
• Confined run and tumble particles with non-Markovian tumbling statistics
• Large deviations in statistics of the local time and occupation time for a run and tumble particle
• Time-dependent properties of run-and-tumble particles: Density relaxation
• Quantifying dissipation in flocking dynamics: When tracking internal states matters
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Interfacial and density fluctuations in a lattice model of motility-induced phase separation
• Entropy production rate in thermodynamically consistent flocks
• Effect of initial conditions on current fluctuations in non-interacting active particles
• Hydrodynamics of a hard-core active lattice gas
• Dynamical patterns and nonreciprocal effective interactions in an active-passive mixture through exact hydrodynamic analysis
• Non-Stationary Critical Phenomena: Expanding The Critical Point
• A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise
• Fluctuating Hydrodynamics Describes Transport in Cellular Aggregates
• On perturbation around closed exclusion processes
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Long-range influence of a pump on a critical fluid