Thermostating by deterministic scattering: Heat and shear flow

We apply a recently proposed thermostating mechanism to an interacting many-particle system where the bulk particles are moving according to Hamiltonian dynamics. At the boundaries the system is thermalized by deterministic and time-reversible scattering. We first show how this scattering mechanism can be related to stochastic boundary conditions. We subsequently simulate thermal conduction and shear flow for a hard disk fluid. By comparing the transport coefficients obtained from computer simulations to theoretical results we find that this thermostating mechanism yields well-defined nonequilibrium steady states in the range of linear response. Furthermore, the conjectured identity between thermodynamic entropy production and exponential phase-space contraction rates is investigated from the standpoint of our formalism. We find that, in general, these quantities do not agree.