Non-equilibrium simulations

Particle methods can be used in non-equilibrium simulations of both microscopic atomistic flows and macroscopic hydrodynamic flows. In the microscopic case, many-body systems can be driven away from equilibrium, into non-equilibrium states, by adding boundary, constraint, or driving forces to the usual atomistic forces: The additional forces can act as energy sources and sinks, with which the driven system can exchange heat, and through which it can perform mechanical work. In adapting similar ‘smoothed-particle’ methods to macroscopic problems, moving boundaries and heat reservoirs can be treated more easily, simply by specifying the velocities and temperatures of special boundary particles. The smoothed-particle technique suggests a natural form of turbulent eddy viscosity which damps the shortest-wavelength hydrodynamic velocity fluctuations. Here, 25 years of development of non-equilibrium particle methods are highlighted, emphasizing the importance of thermostats and boundary conditions to this activity, and illustrating microscopic fractal phase-space distributions and the simulation of macroscopic hydrodynamic instabilities with recent worked-out examples. Some remaining puzzles are given which we hope will be solved in the near-term future.