Deterministic Thermal Reservoirs

We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism for hard disks where the collision rule at the boundary is modified. Numerical evidence and theoretical argument is given that suggests that an energy balance is achieved for a system of hard disks in contact with two reservoirs at equal temperatures. This system however produces entropy near the the system-reservoir boundaries and this entropy flows into the two reservoirs. Thus rather than producing an equilibrium state, the system is at a steady state with a steady entropy flow without any associated energy flux. The microscopic mechanisms associated with energy and entropy fluxes for this system are examined in detail.