2015/07/04 by Hoover, William Graham, Hoover, Carol Griswold
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1507.01645
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, ∝ p2 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 æsthetically 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.