Nonreciprocal Chiral Automata

Abstract

Odd pressure is a parity-odd transport coefficient that gives an isotropic pressure response to vorticity in compressible two-dimensional fluids. By asymmetrically coupling vortical and compressional modes, it provides a direct mechanism for a nonreciprocal hydrodynamic response reminiscent of several biological systems. Yet microscopic models realizing odd pressure as a transport coefficient are relatively scarce. Here, we construct one such model using a lattice-gas cellular automaton based on the Frisch-Hasslacher-Pomeau II model with rest particles and chiral collisions, whose Chapman-Enskog coarse-graining produces a nonzero odd pressure coefficient. The key ingredient is a local parity-breaking collision that weakly rotates moving particles in the presence of a rest particle. At hydrodynamic scales, this microscopic rule acts as an effective magnetic field, converting the model's bulk viscosity into odd pressure. More generally, we derive expressions relating Hall viscosity, odd pressure, and odd torque to their parity-even counterparts in our model.