## 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 120

12) P which, on using the homogeneity of the liquid and the central nature of the

following physical interpretation. With respect to a central molecule, pg(r)4Trr2 dr

...

12) P which, on using the homogeneity of the liquid and the central nature of the

**potential**, can be simplified to / g(r)4Trr2dr = V— — (4.13) v " This result has thefollowing physical interpretation. With respect to a central molecule, pg(r)4Trr2 dr

...

Page 121

*(r) o where a is the intermolecular separation for which the

vanishes. These

of these

radial ...

*(r) o where a is the intermolecular separation for which the

**potential**energyvanishes. These

**potential**functions are shown in Figure 4.1. We shall use someof these

**potentials**later to study the properties of one-dimensional liquids. Theradial ...

Page 127

4.5 TAKAHASHI ONE-DIMENSIONAL FLUID MODELS 4.5.1 Hard-Sphere

models to illustrate the ideas of the previous sections. Consider a line of length L

of rigid ...

4.5 TAKAHASHI ONE-DIMENSIONAL FLUID MODELS 4.5.1 Hard-Sphere

**Potential**In this section, we shall use the exactly soluble one-dimensional fluidmodels to illustrate the ideas of the previous sections. Consider a line of length L

of rigid ...

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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