Hamiltonian dynamics of thermostated systems: Two-temperature heat-conducting [lowercase_phi_synonym]4 chains.

We consider and compare four Hamiltonian formulations of thermostated 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 “[lowercase_phi_synonym]4” 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 Nosé-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. [ABSTRACT FROM AUTHOR]