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American Journal of Physics -- February 2006 -- Volume 74, Issue 2, pp. 123

Teaching the principles of statistical dynamics

Kingshuk Ghosh1, Ken A. Dill1, Mandar M. Inamdar2, Effrosyni Seitaridou2, and Rob Phillips3

1Department of Biophysics, University of California, San Francisco, California 94143
2Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125
3Division of Engineering and Applied Science and Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125

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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 the mass-action laws of chemical kinetics. In analogy with the way that the maximization of entropy over microstates leads to the Boltzmann distribution 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 that 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 that make it possible to observe dynamics one trajectory at a time.

© 2006 American Association of Physics Teachers

KEYWORDS and PACS

Keywords

diffusion, heat transfer, viscosity, reaction kinetics, entropy, statistical distributions, teaching, physics education

PACS

  • 05.40.-a

    Fluctuation phenomena, random processes, noise, and Brownian motion

  • 05.60.-k

    Transport processes

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History
Received May 2005
Accepted Nov 2005
Online Jan 2006

PUBLICATION DATA

ISSN

0002-9505 (print)  

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.2142789

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