## Statistical mechanics: fundamentals and modern applicationsThis book examines the latest developments in statistical mechanics, a branch of physical chemistry and physics that uses statistical techniques to predict the properties and the behavior of chemical and physical systems. It begins with a review of some of the essential concepts and then discusses recent developments in both equilibrium and nonequilibrium statistical mechanics. It covers liquids, phase transitions, renormalization theory, Monte Carlo techniques, and chaos. |

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Page 212

while studying pollen grains and other particles suspended in water and other

fluids under a microscope, observed that their

of ...

**BROWNIAN**.**MOTION**. 9.1 INTRODUCTION In 1827 the botanist Robert Brown,while studying pollen grains and other particles suspended in water and other

fluids under a microscope, observed that their

**motion**was irregular. The**motion**of ...

Page 213

9.2 NATURE OF

water, the water molecules are constantly in motion, bombarding the pollen

grains from all sides with very high frequency. The grains respond to the net

effect of ...

9.2 NATURE OF

**BROWNIAN MOTION**In the case of pollen grains suspended inwater, the water molecules are constantly in motion, bombarding the pollen

grains from all sides with very high frequency. The grains respond to the net

effect of ...

Page 346

13.4.4 Fractal Nature of

equation as a model for

fluctuations y,- relax on a time scale much shorter than that of the particle

fluctuations.

13.4.4 Fractal Nature of

**Brownian Motion**In Chapter 9, we used the Langevinequation as a model for

**Brownian motion**. According to this model, the bathfluctuations y,- relax on a time scale much shorter than that of the particle

fluctuations.

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### Contents

Classical Statistical Mechanics | 3 |

Quantum Statistical Mechanics | 45 |

Phase Transitions and Critical Phenomena | 83 |

Copyright | |

14 other sections not shown

### Common terms and phrases

attractor automata average behavior bifurcation Boltzmann Boltzmann equation Brownian motion Brownian particle BZ reaction calculate called canonical ensemble cell cellular automaton chaos Chapter coefficient collisions configuration consider coordinates correlation functions coupling constants critical exponents critical point defined depends derivation dimension discussed distribution function dynamics eigenvalues entropy equilibrium evaluated example ferromagnetic fixed point fluctuations fluid FORTRAN FORTRAN program fractal free energy frequency Gaussian Hamiltonian initial integral interactions Ising model iterations Kramers Langevin equation lattice limit cycle linear magnetization Markovian matrix method microcanonical ensemble microstates molecular nonequilibrium nonlinear number of particles obtained one-dimensional order parameter oscillations partition function Pathria phase space phase transition polymer potential power spectrum probability density problem protein quantities quantum mechanics RANDOM NUMBER random walk scaling Section shown in Figure simulation solution spin glass statistical mechanics steps stochastic temperature theorem thermodynamic limit total number values vector velocity zero