Convection Patterns in Nonequilibrium Kawasaki Dynamics at Low Temperature

Abstract

We study a conservative stochastic lattice gas (Kawasaki dynamics) coupled in the bulk to a heat bath, which leads to standard phase separation at low uniform temperatures. Instead, a macroscopic temperature gradient drives the system into a nonequilibrium steady state. In this state, the usual long-range order is replaced by robust convection patterns, featuring regularly spaced stripe structures. We show that these nonequilibrium states differ markedly from equilibrium configurations with the same local temperature profiles. Finally, we develop a macroscopic description that captures these behaviors and provides a unified framework for understanding the observed patterns.