Entropy Production and Volume Contraction in Thermostated Hamiltonian Dynamics
Physical Review E
Patra et al. recently showed that the time-averaged rates of entropy production and phase-space volume contraction are equal for several different molecular dynamics methods used to simulate nonequilibrium steady states in Hamiltonian systems with thermostated temperature gradients. This equality is a plausible statistical analog of the second law of thermodynamics. Here we show that those two rates are identically equal in a wide class of methods in which the thermostat variables z are determined by ordinary differential equations of motion (i.e., methods of the Nosé-Hoover or integral feedback control type). This class of methods is defined by three relatively innocuous restrictions which are typically satisfied in methods of this type
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Ramshaw, J.D. 2017. Entropy production and volume contraction in thermostated Hamiltonian dynamics. Physical Review E, 96(5):052122.