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A simple deterministic and time reversal invariant thermostat

A simple deterministic and time reversal invariant type of thermostat is proposed to be used for computer simulations of classical systems. It acts on collisions with the walls of the container exclusively. It maps the incoming and outgoing velocity of an impinging particle onto each other uniquely, in a way that satisfies a detailed balance condition with respect to the (local) wall temperature. It is fast to implement on a computer, leads to rapid equilibration or approach to a stationary nonequilibrium state and it effects the physical properties of the system in a narrow boundary layer only. Because of the deterministic nature it is especially suitable for studying dynamical systems characteristics, such as Lyapunov exponents and fractal dimensions of attractors. A few successful applications have been reported already.