## 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 10

This completes the limiting process, and the resulting distribution [Eq. (1.35)] is

called a

the

This completes the limiting process, and the resulting distribution [Eq. (1.35)] is

called a

**Gaussian**(or normal) distribution. In the case of a continuous variable x,the

**Gaussian**probability density is p(x) 1 2ir exp 2o-2 (1.36) where ju, = (x).Page 11

When a physical event is composed of a series of independent events randomly

distributed according to any distribution with a finite mean and a finite variance,

the probability density is

When a physical event is composed of a series of independent events randomly

distributed according to any distribution with a finite mean and a finite variance,

the probability density is

**Gaussian**. This result is a consequence of the central ...Page 249

Hence, Eq. (10.54) represents the correlation function of a free rotator. Because

Eq. (10.54) is

function will give a

torque ...

Hence, Eq. (10.54) represents the correlation function of a free rotator. Because

Eq. (10.54) is

**Gaussian**, Fourier transformation of the free-rotator correlationfunction will give a

**Gaussian**band shape. At longer times, the mean-squaretorque ...

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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