Ergodicity of a Singly-Thermostated Harmonic Oscillator

Abstract

Although Nose's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nose-Hoover ( harmonic ) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. These models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

Fifteen pages and six figures, accepted 23 August 2015 by Communications in Nonlinear Science and Numerical Simulation

References in corpus (2)

• Non-Ergodicity of Nose-Hoover chain thermostat in computationally achievable time
• Ergodicity of a Time-Reversibly Thermostated Harmonic Oscillator and the 2014 Ian Snook Prize

Cited by in corpus (10)

• The Equivalence of Dissipation from Gibbs' Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators
• Stochastic sampling of the isothermal-isobaric ensemble: phase diagram of crystalline solids from molecular dynamics simulation
• General formalism for singly-thermostated Hamiltonian dynamics
• Dynamic principle for ensemble control tools
• Maximum speed of dissipation
• Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems
• Failure of deterministic and stochastic thermostats to control temperature of molecular systems
• Ergostatting and Thermostatting at a Fixed Point
• Invariant tori for multi-dimensional integrable hamiltonians coupled to a single thermostat
• Singly-Thermostated Ergodicity in Gibbs' Canonical Ensemble and the 2016 Ian Snook Prize Award