2019/06/01 by William G. Hoover, J. C. Sprott, Hoover, William Graham +3
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical Physics (physics.class-ph) #FOS: Physical sciences #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1906.03107
openalex publication_date 2019/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To follow up recent work of Xiao-Song Yang on the Nosé-Hoover oscillator we consider Dettmann's harmonic oscillator, which relates Yang's ideas directly to Hamiltonian mechanics. We also use the Hoover-Holian oscillator to relate our mechanical studies to Gibbs' statistical mechanics. All three oscillators are described by a coordinate q and a momentum p. Additional control variables (ζ, ξ) vary the energy. Dettmann's description includes a time-scaling variable s, as does Nosé's original work. Time scaling controls the rates at which the (q,p,ζ) variables change. The ergodic Hoover-Holian oscillator provides the stationary Gibbsian probability density for the time-scaling variable s. Yang considered \it qualitative features of Nosé-Hoover dynamics. He showed that longtime Nosé-Hoover trajectories change energy, repeatedly crossing the ζ= 0 plane. We use moments of the motion equations to give two new, different, and brief proofs of Yang's long-time limiting result.