Ergodic Time-Reversible Chaos for Gibbs' Canonical Oscillator

William Graham Hoover
Ruby Valley Research Institute, Highway Contract 60, Box 601, Ruby Valley, NV 89833, USA

Julien Clinton Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706, USA

Puneet Kumar Patra
Advanced Technology Development Center, Department of Civil Engineering, Indian Institute of Technology, Kharagpur, West Bengal, 721302, India

Received 20 July 2015
Received in revised form 26 August 2015
Accepted 27 August 2015
Available online 1 September 2015
Communicated by C. R. Doering


Nose's pioneering 1984 work inspired a variety of time-reversible deterministic thermostats. Though several groups have developed successful doubly-thermostated models, single-thermostat models have failed to generate Gibbs' canonical distribution for the one-dimensional harmonic oscillator. A 2001 doubly-thermostated model, claimed to be ergodic, has a singly-thermostated version. Though neither of these models is ergodic this work has suggested a successful route toward singly-thermostated ergodicity. We illustrate both ergodicity and its lack for these models using phase-space cross sections and Lyapunov instability as diagnostic tools.

Ref: W. G. Hoover, J. C. Sprott, and P. K. Patra, Phys. Lett. A 379, 2935-2940 (2015)

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