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The master equation approach to Lyapunov spectra for many-particle systems isapplied to non-equilibrium thermostatted systems to discuss the conjugatepairing rule. We consider iso-kinetic thermostatted systems with a shear flowsustained by an external restriction, in which particle interactions areexpressed as a Gaussian white randomness. Positive Lyapunov exponents arecalculated by using the Fokker-Planck equation to describe the tangent vectordynamics. We introduce another Fokker-Planck equation to describe thetime-reversed tangent vector dynamics, which allows us to calculate thenegative Lyapunov exponents. Using the Lyapunov exponents provided by these twoFokker-Planck equations we show the conjugate pairing rule is satisfied forthermostatted systems with a shear flow in the thermodynamic limit. We alsogive an explicit form to connect the Lyapunov exponents with thetime-correlation of the interaction matrix in a thermostatted system with acolor field.Comment: 10 page

Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostated systems