## Statistical Mechanics and Molecular SimulationsTheoreticians are increasingly being asked to solve problems that cross traditional disciplinary lines. By uniting basic concepts in equilibrium and time-dependent statistical mechanics with modern computational techniques, this book provides a comprehensive view of how theory proceeds from concepts to model construction to practical algorithms. - ;Complex systems that bridge the traditional disciplines of physics, chemistry, biology, and materials science can be studied at an unprecedented level of detail using increasingly sophisticated theoretical methodology and high-speed computers. The aim of this book is to prepare burgeoning users and developers to become active participants in this exciting and rapidly advancing research area by uniting for the first time, in one monograph, the basic concepts of equilibrium and time-dependent statistical mechanics with the modern techniques used to solve the complex problems that arise in real-world applications. The book contains a detailed review of classical and quantum mechanics, in-depth discussions of the most commonly used ensembles simultaneously with modern computational techniques such as molecular dynamics and Monte Carlo, and important topics including free-energy calculations, linear-response theory, harmonic baths and the generalized Langevin equation, critical phenomena, and advanced conformational sampling methods. Burgeoning users and developers are thus provided firm grounding to become active participants in this exciting and rapidly advancing research area, while experienced practitioners will find the book to be a useful reference tool for the field. - |

### What people are saying - Write a review

User Review - Flag as inappropriate

Extraordinary statistical mechanics book as well as its computer simulation theme throughout the book. Tuckerman makes very good connection between principles and practical simulations. I would recommend to everyone who would like to learn how statistical mechanics is applied to simulations. Bravo!

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The most understandable book of statistical physics on simulations I have ever read. Highly recommended!!

### Contents

1 Classical mechanics | 1 |

2 Theoretical foundations of classical statistical mechanics | 53 |

3 The microcanonical ensemble and introduction to molecular dynamics | 74 |

4 The canonical ensemble | 133 |

5 The isobaric ensembles | 214 |

6 The grand canonical ensemble | 261 |

7 Monte Carlo | 277 |

8 Free energy calculations | 312 |

13 Classical timedependent statistical mechanics | 491 |

14 Quantum timedependent statistical mechanics | 526 |

15 The Langevin and generalized Langevin equations | 568 |

16 Critical phenomena | 605 |

Properties of the Dirac deltafunction | 649 |

Evaluation of energies and forces | 652 |

Proof of the Trotter theorem | 663 |

Laplace transforms | 666 |

9 Quantum mechanics | 362 |

10 Quantum ensembles and the density matrix | 391 |

FermiDirac and BoseEinstein statistics | 405 |

12 The Feynman path integral | 442 |

671 | |

687 | |

### Common terms and phrases

algorithm approximation autocorrelation function bath canonical distribution canonical ensemble canonical partition function classical computed conservation consider constant constraint correlation function deﬁned denoted density matrix derivative distribution function eigenvalues eigenvectors equations of motion equilibrium evaluated example expressed factor fermions ﬁrst force frequency given grand canonical ensemble Hamilton’s equations Hamiltonian harmonic oscillator ideal gas initial conditions interactions Ising model isothermal-isobaric isothermal-isobaric ensemble known Laplace transform Liouville microcanonical ensemble microscopic molecular dynamics molecular dynamics calculation molecule momenta momentum Monte Carlo non-Hamiltonian Nosé–Hoover Note obtain one-dimensional operator particle path integral perturbation phase space physical potential energy pressure problem propagator reaction coordinate sampling Section simple simulation solution solved spin statistical mechanics temperature theorem thermodynamic thermostat trajectory variables vector velocity Verlet virial volume yields