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In response to W. G. Hoover's comment [arXiv:1204.0312v2] on our work[arXiv:1203.5968], we show explicitly that the divergence of the velocity fieldassociated with the Nos\'e-Hoover equations is nonzero, implying that thoseequations are not volume preserving, and hence, as often stated in theliterature, are not Hamiltonian. We further elucidate that the trajectories{q(t)} generated by the Nos\'e-Hoover equations are generally not identical tothose generated by Dettmann's Hamiltonian. Dettmann's Hamiltonian produces thesame trajectories as the Nos\'e-Hoover equations only on a specific energyshell, but not on the neighboring ones. This fact explains why theNos\'e-Hoover equations are not volume preserving. The Hamiltonian that we putforward with [arXiv:1203.5968] instead produces thermostated dynamicsirrespective of the energy value. The main advantage of our Hamiltonianthermostat over previous ones is that it contains kinetic energy terms that areof standard form with coordinate-independent masses and consequently is readilymatched in laboratory experiments.

Reply to W. G. Hoover [arXiv:1204.0312v2]