Time-Reversible Ergodic Maps and the 2015 Ian Snook Prize

TL;DR

This paper discusses the development of time-reversible dissipative maps in nonequilibrium dynamical systems, highlighting their aesthetic attractor-repellor pairs and challenging researchers to explore these maps, linked to the 2015 Snook-Prize.

Contribution

It introduces time-reversible dissipative maps for nonequilibrium systems and presents the 2015 Snook-Prize challenge to find and analyze such maps.

Findings

Time-reversible maps produce attractor-repellor pairs.

Weak control of temperature achieves ergodicity.

The paper presents a challenge to explore these maps.

Abstract

The time reversibility characteristic of Hamiltonian mechanics has long been extended to nonHamiltonian dynamical systems modeling nonequilibrium steady states with feedback-based thermostats and ergostats. Typical solutions are multifractal attractor-repellor phase-space pairs with reversed momenta and unchanged coordinates, $(q,p)\longleftrightarrow (q,-p)$ . Weak control of the temperature, $\propto p^2$ and its fluctuation, resulting in ergodicity, has recently been achieved in a three-dimensional time-reversible model of a heat-conducting harmonic oscillator. Two-dimensional cross sections of such nonequilibrium flows can be generated with time-reversible dissipative maps yielding \ae sthetically interesting attractor-repellor pairs. We challenge the reader to find and explore such time-reversible dissipative maps. This challenge is the 2015 Snook-Prize Problem.