Ensembles and Stochastic Processes

Abstract

The study of matter which is large with respect to molecular size is one of the oldest of the sciences. It originated in the early metallurgy of China and the Middle East and permeates modern research in both the physical and biological sciences. From a theoretical point of view, the reversible or mechanical properties of matter were the first to be understood. These are the properties characterized by Newton’s laws of motion which relate forces, velocities, and spatial positions. These properties are termed reversible because if one reverses all velocities, the magnetic field, and the time, the resulting motion is the reverse of what was observed up to that time—like seeing a movie run backwards. This reversibility of the mechanical theory suggested for many years that any observable motion should have a twin reversed motion which can also be observed. The consequences of reversibility, however, seem contrary to our intuition: Although salt spontaneously dissolves in water, no one has ever seen salt precipitate from an unsaturated solution.