Another Hamiltonian "Thermostat" - Comments on arXiv Contributions   1203.5968, 1204.4412, 1205.3478, and 1206.0188
  Campisi, Zhan, Talkner, and Haenggi state, in promoting a new logarithmic computational thermostat [ arXiv 1203.5968 and 1204.4412 ], that (thermostated) Nose-Hoover mechanics is not Hamiltonian. First I point out that Dettmann clearly showed the Hamiltonian nature of Nose-Hoover mechanics. The trajectories {q(t)} generated by Dettmann's Hamiltonian are identical to those generated by Nose-Hoover mechanics. I also observe that when the (Hamiltonian) Campisi thermostat is applied to "nonequilibrium" heat transfer problems some very interesting, and somewhat paradoxical, phase portraits can result. See too Marc Mel\'endez' nice arXiv 1205.3478 and our joint work 1206.0188 . 
Wm. G. Hoover
cond-mat.stat-mech nlin.CD physics.class-ph