Supplementary Material

Thermostatting Nonequilibrium Systems: A Thermal Energy Constraint for Systems under Directive Perturbations. Supplementary Materials include a proof that neither the work nor the dissipation are computable a priori, an initial condition sensitivity study, examples of numerical issues arising from directive perturbations, a timestep size sensitivity study, the effects of including approximations of the streaming/advective momentum, the extension to weakly directive perturbations, the behavior of unperturbed thermostatted - i.e. equilibrium - systems, and the behavior of perturbed unthermostatted systems.