Nonequilibrium Thermodynamics and Nose-Hoover Dynamics

We show that systems driven by an external force and described Delta S-i = k(b)D[integral(t,Gamma(t)) parallel to integral(s) (t, Gamma(s)(t))integral(eq)(r) (zeta(t))]>= 0 by Nose Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical equilibrium. By treating the real variables as the system and the thermostatted variable as the reservoir, we establish the first and second law of thermodynamics. As for Hamiltonian systems, the entropy production can be expressed as a relative entropy measuring the system reservoir correlations established during the dynamics.