We consider and compare four Hamiltonian formulations of fhermostated mechanics,three of them kinetic,and the other one configurational.Though all four approaches "work" at equilibrium,their application to many-body nonequilibrium simulations can fail to provide a proper flow of heat.All the Hamiltonian formulations considered here are applied to the same prototypical two-temperature "phi4"model of a heat-conducting chain.This model incorporates nearest-neighbor Hooke's-Law interactions plus a quartic tethering potential.Physically correct results,obtained with the isokinetic Gaussian and Nose-Hoover thermostats,are compared with two other Hamiltonian results.The latter results,based on constrained Hamiltonian thermostats,fail to model correctly the flow of heat.
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