# The Equivalence of Dissipation from Gibbs' Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators

@article{Patra2015TheEO, title={The Equivalence of Dissipation from Gibbs' Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators}, author={Puneet Kumar Patra and William Graham Hoover and Carol Griswold Hoover and Julien Clinton Sprott}, journal={Int. J. Bifurc. Chaos}, year={2015}, volume={26}, pages={1650089:1-1650089:11} }

Gibbs' thermodynamic entropy is given by the logarithm of the phase volume, which itself responds to heat transfer to and from thermal reservoirs. We compare the thermodynamic dissipation described by phase-volume loss with heat-transfer entropy production. Their equivalence is documented for computer simulations of the response of an ergodic harmonic oscillator to thermostated temperature gradients. In the simulations one or two thermostat variables control the kinetic energy or the kinetic…

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