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

Tooru Taniguchi·Gary P. Morriss
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Abstract

The master equation approach to Lyapunov spectra for many-particle systems is applied to non-equilibrium thermostatted systems to discuss the conjugate pairing rule. We consider iso-kinetic thermostatted systems with a shear flow sustained by an external restriction, in which particle interactions are expressed as a Gaussian white randomness. Positive Lyapunov exponents are calculated by using the Fokker-Planck equation to describe the tangent vector dynamics. We introduce another Fokker-Planck equation to describe the time-reversed tangent vector dynamics, which allows us to calculate the negative Lyapunov exponents. Using the Lyapunov exponents provided by these two Fokker-Planck equations we show the conjugate pairing rule is satisfied for thermostatted systems with a shear flow in the thermodynamic limit. We also give an explicit form to connect the Lyapunov exponents with the time-correlation of the interaction matrix in a thermostatted system with a color field.

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Tooru Taniguchi, Gary P. Morriss. 2002-04-03. Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems. https://doi.org/10.1103/physreve.66.066203

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