THE CONJUGATE-PAIRING RULE FOR NON-HAMILTONIAN SYSTEMS

In systems that satisfy the Conjugate Pairing Rule (CPR), the spectrum of Lyapunov exponents is symmetric. The sum of each conjugate pair of exponents is identical. Since in dissipative systems the sum of all t he exponents is the entropy production divided by Boltzmann's constant , the calculation of transport coefficients from the Lyapunov exponent s is greatly simplified in systems that satisfy CPR. Sufficient condit ions for CPR are well known: the underlying adiabatic dynamics should be symplectic, However, the necessary conditions for CPR are not known . In this paper we report on the results of computer simulations which shed light on the necessary conditions for the CPR to hold. We provid e, for the first time, convincing evidence that the standard molecular dynamics algorithm for calculating shear viscosity violates the CPR, even in the thermodynamic limit. In spite of this it appears that the sum of the maximal exponents is equal to the entropy production per de gree of freedom. Thus it appears that the shear viscosity can still be calculated using the standard viscosity algorithm by summing the maxi mal pair of exponents, (C) 1998 American Institute of Physics.