Hoover, W.R.: Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31, 1695

Physical Review A (Impact Factor: 2.81). 04/1985; 31(3):1695-1697. DOI: 10.1103/PhysRevA.31.1695
Source: PubMed


Nose has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with V¹D/ in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta p/sub s/ and p/sub v/. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, p/sub x/, V, epsilon-dot, and zeta, where the x are reduced distances and the two variables epsilon-dot and zeta act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.

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Available from: William Graham Hoover, Aug 07, 2014
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    • "Specifically, by comparing the actual heat flow with the preset value, we can adjust the frequency of the velocity-exchange in real time and achieve that preset heat flow. Total energy and momentum of the system are conserved during the velocity-exchange, while the system temperature is kept at T ave using the Nosé–Hoover thermostat method [43]. "
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    • "Here N, P, and T denote the number of atoms, pressure, and temperature, respectively. Nosé–Hoover thermostat is utilized to keep constant temperature [47] [48]. Parrinello–Rahman technique is adopted to control the stress tensor [49]. "
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