Statistical Mechanics Of Irreversible Processes In Crystals

Statistical Mechanics of Irreversible Processes in Crystals

Irreversible phenomena in crystals, which are not related to processes involving energy dissipation, are studied. An infinite three-dimensional assembly of narmonic oscillators is studied; their position and velocities are considered as random variables whose probability distributions are known at the initial moment. The asymptotic values of these distribution functions can be calculated by solving the equations of motion of the lattice points in terms of the initial conditions. 'Influence functions' are introduced, which are related to the frequency spectrum of the lattice. The second moments are shown to be quasi-invariant, i.e. they tend to a definite asymtotic value after a more or less complicated variation. No other condition is imposed on the initial distribution functions than the absence of correlation at large distances. If they are such that the equipartition of the energy is initially achieved between the normal modes, without any correlation between their phases, all the various moments and local distribution functions tend to their equilibrium value.

Statistical Physics Of Crystals And Liquids: A Guide To Highly Accurate Equations Of State

This important book presents a unified formulation from first principles of the Hamiltonian and statistical mechanics of metallic and insulating crystals, amorphous solids, and liquids. Extensive comparison of theory and experiment provides an accurate understanding of the statistical properties of phonons, electrons, and phonon-phonon and electron-phonon interactions in elemental crystals and liquids. Questions are posed along the following lines: What is the “best” theory for a given property? How accurate is a good theory? What information is gained by a comparison of theory and experiment? How accurate is a good experiment?

Technical Abstract Bulletin