Nonequilibrium systems: hard disks and harmonic oscillators near and far from equilibrium

Abstract

We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and four-dimensional phase spaces. These models provide us with a basis for understanding equilibration and thermodynamic irreversibility in terms of Lyapunov instability, fractal distributions and thermal constraints.

Keywords:

• Chaos
• ergodicity
• thermostats
• reversibility

Acknowledgements

We wish to thank Puneet Patra and Baidurya Bhattacharya for their fresh look at ergodicity described in their 2014 and 2015 Journal of Chemical Physics papers. This stimulation led to some of the advances described here. We thank Jerome Delhommelle for encouraging our work on this paper. We also thank John Ramshaw for useful discussions relating to Liouville’s Theorem as well as for furnishing us a computer program providing the finite-difference results described in this paper.

Notes

No potential conflict of interest was reported by the authors.