## 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 16

This approach is more general, puts the coordinates and momenta on an equal

footing, has the conservation laws built in, and affords a relatively smooth

transition to quantum statistical mechanics. We begin with a summary of the

This approach is more general, puts the coordinates and momenta on an equal

footing, has the conservation laws built in, and affords a relatively smooth

transition to quantum statistical mechanics. We begin with a summary of the

**Hamiltonian**...Page 58

For now, we retain the general mean-field case. Since the particles are

independent, the total

particle operators N M = ^ ^k (2.43) such that, for the fcth particle, 3<kWi) = e,k> (

2.44) where e ...

For now, we retain the general mean-field case. Since the particles are

independent, the total

**Hamiltonian**operator separates into the sum of N one-particle operators N M = ^ ^k (2.43) such that, for the fcth particle, 3<kWi) = e,k> (

2.44) where e ...

Page 107

From various studies, it has been found that the exponents depend on the

symmetry of the

range of interactions (Fisher, 1974). We discuss each of these in turn now. 3.4.4

Symmetry ...

From various studies, it has been found that the exponents depend on the

symmetry of the

**Hamiltonian**, on the dimensionality of the system, and on therange of interactions (Fisher, 1974). We discuss each of these in turn now. 3.4.4

Symmetry ...

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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