Chapter 4
Random walks, friction, and
diffusion
It behoves us to remember that in physics it has taken great
scientists to discover simple things. They are very great names
indeed which we couple with the explanation of the path of a
stone, the droop of a chain, the tints of a bubble, the shadows
in a cup. – D’Arcy Thompson, 1917Section 3.2.5 argued that the origin of friction was the conversion of organized motion to disor-
dered motion by collisions with a surrounding, disordered medium. In this picture, the First Law
of thermodynamics is just a restatement of the conservation of energy. To justify such a unifying
conclusion, we’ll continue to look for nontrivial, testable, quantitative predictions from the model.
This process is not just an exercise in retracing others’ historical footsteps. Once we understand
the origin of friction, a wide variety of otherdissipative processes—those that irreversibly turn
order into disorder—will make sense, too:
- The diffusion of ink molecules in water erases order, for example any pattern initially present
(Section 4.4.2). - The conduction of heat erases the initial separation into hot and cold regions (Section 4.6.4).
- Friction erases order in the initial directedmotionof an object (Section 4.1.4).
- Electrical resistance runs down your flashlight batteries, making heat (Section 4.6.4).
In every case just listed, organized kinetic or potential energy gets degraded into mass, average,
disorganized motion, by collisions with a large, random environment. The paradigm we will study
for all of these processes will bethe physics of the random walk(Section 4.1.2).
None of the dissipative processes listed above matters much for the Newtonian questions of
celestial mechanics. But all will turn out to be of supreme importance in understanding the physical
world of cells. The difference is that in cells, the key actors are single molecules or perhaps structures
of at most a few thousand molecules. In this nanoworld, the tiny energykBTrisnotso tiny; the
©c2000 Philip C. Nelson