Hamiltonian Dynamics of Thermostated Systems: Two-Temperature Heat-Conducting phi-4 Chains

Abstract

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 "phi-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 Nose-Hoover thermostats, are compared with two other Hamiltonian results. The latter results, based on constrained Hamiltonian thermostats, fail correctly to model the flow of heat.

15 pages, 6 figures, in honor of Prof Harald Posch Birthday #65

References in corpus (2)

• Non-Equilibrium Steady States and Transport in the Classical Lattice ${\varphi }^4$ Theory
• Violations of local equilibrium and linear response in classical lattice theories

Cited by in corpus (8)

• Configurational Temperature Control for Atomic and Molecular Systems
• Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient
• Hamiltonian Thermostats Fail to Promote Heat Flow
• Bulgac-Kusnezov-Nosé-Hoover thermostats
• Phase space structure and dynamics for the Hamiltonian isokinetic thermostat
• Heat pump without particle transport or external work on the medium achieved by differential thermostatting of the phase space
• Failure of Logarithmic Oscillators to Thermostat Small Atomic Clusters
• Gradient and Hessian-Based Temperature Estimator in Lattice Gauge Theories: A Diagnostic Tool for Stability and Consistency in Numerical Simulations