ABSTRACT Throughout Boltzmann`s life-long atomistic study of irreversibility, he emphasized the one-body distribution function f1(q,p,t), an average over many particles, with the underlying many-body dynamics taken to be a series of two-body collisions. His derivation of the H Theorem, linking dynamics and thermodynamics, remains the major accomplishment in understanding the Second Law of Thermodynamics. Today Boltzmann`s analytic one-body approach has largely been superceded by using fast computers to simulate many-body “Molecular Dynamics”. Fermi originated Molecular Dynamics at Los Alamos in 1953. His few-body one-dimensional chains launched a generation of numerical studies of Lyapunov-unstable ordinary differential equations. By 1972 computers could simulate 1000-body gases, liquids, or solids, and a new nonequilibrium mechanics was developing to facilitate this work. In 1984, Nosé made a major contribution. He showed how to introduce macroscopic variables, such as temperature, the pressure tensor, and the heat flux, directly into time-reversible microscopic equations of motion. When Nosé`s mechanics is applied to nonequilibrium systems zero-volume “strange attractors” form in the many-body phase space. The attractors provide a new explanation for the classical problem of irreversibility that fascinated Boltzmann. Here I trace the evolution of molecular dynamics from Fermi`s work at Los Alamos to Nosé`s recent work, and I speculate on the applicability of the new nonequilibrium ideas to quantum systems.
Buy this Article
|