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Non-equilibrium Thermodynamics and Statistical MechanicsFoundations and Applications$
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Phil Attard

Print publication date: 2012

Print ISBN-13: 9780199662760

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199662760.001.0001

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Non-Equilibrium Computer Simulation Algorithms

Non-Equilibrium Computer Simulation Algorithms

(p.389) Chapter 11 Non-Equilibrium Computer Simulation Algorithms
Non-equilibrium Thermodynamics and Statistical Mechanics

Phil Attard

Oxford University Press

Three non-equilibrium computer simulation algorithms are presented in detail: stochastic molecular dynamics, non-equilibrium Monte Carlo, and Brownian dynamics. Stochastic molecular dynamics is based on the stochastic dissipative equations of motion, which do not suffer the disadvantages of non-Hamiltonian deterministic equations or thermostats. Extensive numerical tests are performed for steady heat flow and for a driven Brownian particle in a solvent. A non-equilibrium Monte Carlo algorithm is based upon the non-equilibrium probability distribution. Umbrella sampling and other methods to improve the efficiency of the algorithm are discussed. Results are compared with the stochastic molecular dynamics and with Nose-Hoover equilibrium molecular dynamics. Brownian dynamics using the simple Langevin equation is outlined. The perturbation theory of the preceding chapter is used for a more advanced algorithm suited for concentrated dispersions and macromolecules. The stochastic calculus is discussed in the context of Brownian dynamics and the generalised Langevin equation

Keywords:   non-equilibrium, simulation, molecular dynamics, Monte Carlo, Brownian dynamics, stochastic calculus

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