## 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 198

dependence of the molecular statistical distribution function. The phase space of

interest for

**Boltzmann's equation**represents an attempt to get an expression for the timedependence of the molecular statistical distribution function. The phase space of

interest for

**Boltzmann's equation**is ju, space (see Section 1.6.3). Boltzmann ...Page 202

Recall that, in ju, space, dr dv = dx dy dz dvx dvy dvz Our task is to find an

equation for /(r, v, t) as it changes in time and space. ... and collisions due to 202

THE

Recall that, in ju, space, dr dv = dx dy dz dvx dvy dvz Our task is to find an

equation for /(r, v, t) as it changes in time and space. ... and collisions due to 202

THE

**BOLTZMANN EQUATION Boltzmann Equation**, Derivation of**Boltzmann****Equation**,Page 210

It is a fundamental

assumption, in which case the distribution of velocities is given by the Maxwell-

...

It is a fundamental

**equation**in fluid dynamics. If one makes the local equilibriumassumption, in which case the distribution of velocities is given by the Maxwell-

**Boltzmann**distribution [Eq. (1.103)], but the temperature and the average velocity...

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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