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Entropy Production and Volume Contraction in Thermostated Hamiltonian Dynamics
Physical Review E
  • John D. Ramshaw, Portland State University
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Publication Date
  • Nonequilibrium thermodynamics,
  • Hamiltonian systems,
  • Differential equations,
  • Molecular dynamics

Patra et al. [Int. J. Bifurcat. Chaos 26, 1650089 (2016)] 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


This is the publisher's final PDF. Article appears in Physical Review A ( and is copyrighted by APS Journals ( and is available online

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Ramshaw, J.D. 2017. Entropy production and volume contraction in thermostated Hamiltonian dynamics. Physical Review E, 96(5):052122.