## 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 232

9.8 BROWNIAN MOTION AND IRREVERSIBILITY A Brownian particle undergoes

irreversible, random movements. For this reason, theories of Brownian motion

are intimately bound to theories of irreversible

...

9.8 BROWNIAN MOTION AND IRREVERSIBILITY A Brownian particle undergoes

irreversible, random movements. For this reason, theories of Brownian motion

are intimately bound to theories of irreversible

**behavior**. Approaches that explain...

Page 276

(1 - l/a*)1/2 a* > 1 1 ' ' (11.66) a* < 1 We see that for infinite y*, the rate has a

singular

the value 0, but the derivative of the rate is infinite for a* > 1 and zero otherwise.

(1 - l/a*)1/2 a* > 1 1 ' ' (11.66) a* < 1 We see that for infinite y*, the rate has a

singular

**behavior**at the point a* = 1 . At this point, the rate is continuous, havingthe value 0, but the derivative of the rate is infinite for a* > 1 and zero otherwise.

Page 303

This complexity includes multiple periodic oscillations, multiple bifurcations, and

sometimes chaotic

BZ reaction discussed in Section 12.6. In order to understand this more complex

...

This complexity includes multiple periodic oscillations, multiple bifurcations, and

sometimes chaotic

**behavior**. Such complex**behavior**has been observed in theBZ reaction discussed in Section 12.6. In order to understand this more complex

...

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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