Odd fluids from chiral cellular automata

Abstract

Cellular automata are discrete dynamical systems defined on a lattice, in which each site carries a finite set of states that evolve in time according to local deterministic rules. An important application of cellular automata is in lattice gas models of fluids, where the cellular automaton framework provides a particle-based microscopic description of hydrodynamic behavior. The macroscopic fluid equations emerge after coarse-graining over many lattice sites and time steps, offering a bottom-up route to hydrodynamics. A celebrated example is the Frisch-Hasslacher-Pomeau (FHP) model, an automaton defined on a two-dimensional triangular lattice that yields the two-dimensional Navier-Stokes equations upon coarse-graining. In this work, we construct a parity-breaking generalization of the FHP model through two modifications: introducing chiral two-body collision rules and systematically rotating particle velocities to mimic the effect of a background magnetic field. We show that this automaton yields a hydrodynamic model with odd viscosity, a transverse transport coefficient that is a hallmark of odd fluids. We verify the analytical transport coefficients using Poiseuille-flow simulations of the chiral FHP automaton. Our results demonstrate that the chiral automaton introduced here provides a bridge between microscopic parity-breaking scattering processes and macroscopic odd-fluid hydrodynamics.