## 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 15

In this case, when the joint distribution of two variables is simply the product of

their individual distributions, the two ... (1.47) Now consider a random variable J2i

=\ %» which is the

In this case, when the joint distribution of two variables is simply the product of

their individual distributions, the two ... (1.47) Now consider a random variable J2i

=\ %» which is the

**total number**of steps to the right after a**total number**ofN steps.Page 34

Following the procedure in Section 1 .6.2, one may calculate the fluctuations in

the energy of a single molecule. ... on the generalized coordinates through strictly

conserved quantities, such as the total energy or the

Following the procedure in Section 1 .6.2, one may calculate the fluctuations in

the energy of a single molecule. ... on the generalized coordinates through strictly

conserved quantities, such as the total energy or the

**total number**of particles.Page 134

We get 8x Sk(x) « — P(k) (4.65) a The

x + 8x is given by summing Eq. (4.65). The

and x + 8x is also given by pg(x)Sx, by definition. Therefore, pg(x)8x = ^Sk(x) ...

We get 8x Sk(x) « — P(k) (4.65) a The

**total number**of particles in the range x andx + 8x is given by summing Eq. (4.65). The

**total number**of particles in the range xand x + 8x is also given by pg(x)Sx, by definition. Therefore, pg(x)8x = ^Sk(x) ...

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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