Teaching the Principles of Statistical Dynamics

Abstract

We describe a simple framework for teaching the principles that underlie the dynamical laws of transport: Fick's law of diffusion, Fourier's law of heat flow, the Newtonian viscosity law, and mass-action laws of chemical kinetics. In analogy with the way that the maximization of entropy over microstates leads to the Boltzmann law and predictions about equilibria, maximizing a quantity that E. T. Jaynes called "Caliber" over all the possible microtrajectories leads to these dynamical laws. The principle of Maximum Caliber also leads to dynamical distribution functions which characterize the relative probabilities of different microtrajectories. A great source of recent interest in statistical dynamics has resulted from a new generation of single-particle and single-molecule experiments which make it possible to observe dynamics one trajectory at a time.