Canonical dynamics: Equilibrium phase-space distributions

@article{Hoover1985, abstract = {Nos\'{e} 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 V 1/ D 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 s and p 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 x ; V ; ε̇ ; and ζ ; where the x are reduced distances and the two variables ε̇ and ζ 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.}, author = {Hoover, William G. }, citeulike-article-id = {1886058}, comment = {nose-hoover thermostat intro}, doi = {10.1103/PhysRevA.31.1695}, journal = {Physical Review A}, keywords = {algorithms, masters, md}, month = {March}, number = {3}, pages = {1695+}, posted-at = {2008-04-02 10:22:24}, priority = {4}, publisher = {American Physical Society}, title = {{Canonical dynamics: Equilibrium phase-space distributions}}, url = {http://dx.doi.org/10.1103/PhysRevA.31.1695}, volume = {31}, year = {1985} }

TY - JOUR ID - Hoover1985 L3 - citeulike-article-id:1886058 TI - {Canonical dynamics: Equilibrium phase-space distributions} JF - Physical Review A VL - 31 IS - 3 SP - 1695 PB - American Physical Society N2 - Nosé 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 V 1/ D 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 s and p 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 x ; V ; ε̇ ; and ζ ; where the x are reduced distances and the two variables ε̇ and ζ 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. KW - algorithms KW - masters KW - md N1 - nose-hoover thermostat intro AU - Hoover, William PY - 1985/03// UR - http://dx.doi.org/10.1103/PhysRevA.31.1695 ER -