Another Hamiltonian "Thermostat" - Comments on arXiv Contributions 1203.5968, 1204.4412, 1205.3478, and 1206.0188

TL;DR

This paper clarifies misconceptions about the Hamiltonian nature of Nose-Hoover mechanics, discusses the properties of Campisi's logarithmic thermostat, and explores intriguing phase portraits in nonequilibrium heat transfer scenarios.

Contribution

It corrects the claim that Nose-Hoover mechanics is non-Hamiltonian and highlights the Hamiltonian equivalence shown by Dettmann, while also examining the behavior of Campisi's thermostat in nonequilibrium conditions.

Findings

Dettmann's Hamiltonian trajectories match Nose-Hoover mechanics.

Campisi's thermostat can produce paradoxical phase portraits.

Nose-Hoover mechanics is indeed Hamiltonian, contrary to some claims.

Abstract

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 .