Chapter 7

Entropic forces at work

If someone points out to you that your pet theory of the Uni-

verse is contradicted by experiment, well, these experimentalists

do bungle things sometimes. But if your theory is found to be

against the Second Law I can give you no hope; there is noth-

ing for it but to collapse in deepest humiliation. – Sir Arthur

Eddington

Chapter 6 argued that all transactions in a fixed-temperature system are paid for in a single
unified currency, the free energyF=E−TS.The irreversible processes discussed up to that point
emerge as particular cases. For example, a freely falling rock converts its gravitational potential
energy to kinetic energy, with no net change in the mechanical energyE.Ifitlands in mud, however,
its organized kinetic energy gets irreversibly converted to thermal form, loweringEand henceF.
Similarly, ink diffuses in water to maximize its entropy, raisingSand hence again loweringF.
More generally, ifbothenergy and entropy change, a macroscopic system in contact with a thermal
reservoir will change to lower its free energy, even if

• the change actually increases the energy (but increasesTSmore), or


• the change actually decreases the disorder (but decreasesE/Tmore).

In first-year physics the change in potential energy as some state variable changes is called a
“mechanical force.” More precisely, we write

f=−dU/dx.

Section 6.5.2 extended this identification to statistical systems, starting with the simplest sort of
entropic force,namely gas pressure. We found that the force exerted by a gas can be regarded as
the derivative of−Fwith respect to the position of a confining piston. This chapter will elaborate
the notion of an entropic force, extending it to cases of greater biological relevance. For example,
Chapter 2 claimed that the amazing specificity of enzymes and other molecular devices stems
from the precise shapes of their surfaces, and from short-range physical interactions between those
surfaces and the molecules on which they act. This chapter will explore the origins of some of these

©c2000 Philip C. Nelson

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