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We compute the full Lyapunov spectra for a hard-disk fluid under temperaturegradient and shear. The system is thermalized by deterministic andtime-reversible scattering at the boundary. This thermostating mechanism allowsfor energy fluctuations around a mean value which is reflected by only twovanishing Lyapunov exponents in equilibrium and nonequilibrium. The Lyapunovexponents are calculated with a recently developed formalism for systems withelastic hard collisions. In a nonequilibrium steady state the average phasespace volume is contracted onto a fractal attractor leading to a negative sumof Lyapunov exponents. Since the system is driven inhomogeneously we do notexpect the conjugate pairing rule to hold which is confirmed numerically.

Lyapunov Instability for a hard-disk fluid in equilibrium and nonequilibrium thermostated by deterministic scattering