## 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 254

The

correlation functions gives the polymer dynamics and is the

problem. Bixon (Bixon, 1973) and Zwanzig (Zwanzig, 1974) have discussed this

The

**solution**of Eq. (10.68) for the normal coordinates and their correspondingcorrelation functions gives the polymer dynamics and is the

**solution**of ourproblem. Bixon (Bixon, 1973) and Zwanzig (Zwanzig, 1974) have discussed this

**solution**...Page 294

25, and so on. The

of A give critical points that are called repellers in that all

**Solutions**exist for a = 1 and b > 4, a = 2 and b > 9,a = 3 and ft > 16, a = 4 and b >25, and so on. The

**solutions**X = ai exp(Af) and y = a2 exp(A?) for positive valuesof A give critical points that are called repellers in that all

**solutions**are repelled ...Page 305

It is much easier to obtain maps of difference equations than it is to obtain the

difference equation that shows all the complexity of a multidimensional

differential ...

It is much easier to obtain maps of difference equations than it is to obtain the

**solutions**of ODEs. For this reason, we now consider a simple one-dimensionaldifference equation that shows all the complexity of a multidimensional

differential ...

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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