## Statistical Mechanics of Nonequilibrium LiquidsIn recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate-level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration. |

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### Contents

6 | |

Linear irreversible thermodynamics | 11 |

The microscopic connection | 33 |

The Greenkubo relations | 79 |

Linearresponse theory | 95 |

Computer simulation algorithms | 119 |

Nonlinear response theory | 167 |

Dynamical stability | 209 |

Nonequilibrium ﬂuctuations | 259 |

Thermodynamics of steady states | 283 |

301 | |

309 | |

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### Common terms and phrases

¼ ð ¼À ÀÁ adiabatic algorithm attractor autocorrelation function boundary conditions calculate canonical ensemble conjugate consider constant constitutive relation constraint correlation function deﬁned deﬁnition density derivative difﬁculty dimension dissipative eigenvalues entropy equations of motion ergodic Evans and Morriss evolution exponential expression external ﬁeld Figure ﬁnite ﬁrst ﬁxed ﬂuctuation theorem ﬂuid ﬂux force Gauss Gaussian isokinetic gives Green–Kubo relations Hamiltonian inﬁnite initial integral internal energy Jarzynski equality Kawasaki kinetic energy Langevin equation Lennard–Jones linear response theory Liouville equation Liouvillean Lyapunov exponents microscopic molecular dynamics momenta momentum Navier–Stokes NEMD nonequilibrium steady nonequilibrium systems nonlinear response obtained operator particle perturbation phase point phase space phase variable planar Couette ﬂow pressure tensor propagator Section shear rate shear stress shear viscosity SLLOD equations steady-state streaming velocity sufﬁciently tensor thermal thermodynamic temperature thermostat time-dependent trajectory transport coefﬁcients TTCF unstable manifolds vector XN i¼1 zero

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Page i - Engineers, a Fellow of the Institute of Physics, and a Member of the Institute of Welding.

Page i - D., has been a lecturer in the School of Physics at the University of New South Wales, Australia, since 1990.

Page 1 - Mechanics provides a complete microscopic description of the state of a system. When the equations of motion are combined with initial conditions and boundary conditions, the subsequent time evolution of a classical system can be predicted. In systems with more than just a few degrees of freedom such an exercise is impossible.

Page 1 - ... for such systems. Thermodynamics provides a theoretical framework for correlating the equilibrium properties of such systems. If the system is not at equilibrium, fluid mechanics is capable of predicting the macroscopic nonequilibrium behaviour of the system.