## 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 310

1.0 0.8 0.6 P X 0.4 - 0.2 - 3.0 3.2 3.4 3.6 3.8 a Figure 12.14

the logistic equation. 4.0 1992, pp. 77-78; Drazin, 1993, p. 95). Each point on this

diagram represents a fixed point for a given value of a. At a = 3.0 a period

doubling occurs. At a = 3.45 the system again undergoes period doubling, and

doubling continues till chaos ensues. This diagram is very complex, and includes

both even and odd periods that show several chaotic regions. The odd periods

require ...

1.0 0.8 0.6 P X 0.4 - 0.2 - 3.0 3.2 3.4 3.6 3.8 a Figure 12.14

**Bifurcation**diagram ofthe logistic equation. 4.0 1992, pp. 77-78; Drazin, 1993, p. 95). Each point on this

diagram represents a fixed point for a given value of a. At a = 3.0 a period

doubling occurs. At a = 3.45 the system again undergoes period doubling, and

doubling continues till chaos ensues. This diagram is very complex, and includes

both even and odd periods that show several chaotic regions. The odd periods

require ...

Page 316

Usually, for a given experiment, the temperature, stirring rate, and initial

concentrations are fixed, and the flow rate is taken to be the

. All the

These include primary and secondary Hopf

tangent

doubling via flip

seemingly periodic ...

Usually, for a given experiment, the temperature, stirring rate, and initial

concentrations are fixed, and the flow rate is taken to be the

**bifurcation**parameter. All the

**bifurcations**discussed above have been observed in the BZ reaction.These include primary and secondary Hopf

**bifurcations**, flip**bifurcations**, andtangent

**bifurcations**. Routes to chaos that have been observed include perioddoubling via flip

**bifurcations**and intermittency. When intermittency is present, aseemingly periodic ...

Page 321

There have been some attempts to study the

the

the system is deterministic. Similar to the critical point of a continuous phase

transition (see Section 3.2.4), fluctuations become very large near

points. It is possible to apply renormalization group theory (see Section 3.5) to

dimensional map of ...

There have been some attempts to study the

**bifurcation**mechanisms. It is here atthe

**bifurcation**points that the system is stochastic, while in between these pointsthe system is deterministic. Similar to the critical point of a continuous phase

transition (see Section 3.2.4), fluctuations become very large near

**bifurcation**points. It is possible to apply renormalization group theory (see Section 3.5) to

**bifurcation**points (Drazin, 1993, Section. Figure 12.23 First-return one-dimensional map of ...

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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

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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