Chapter 6

Entropy, temperature, and free

energy

The axiomatic method has many advantages, which are similar

to the advantages of theft over honest work. – Bertrand Russell

It’s time to come to grips with the still rather woolly ideas proposed in Chapter 1, and turn
them into precise equations. We can do it, starting from the statistical ideas developed in our study
of the ideal gas law and Brownian motion.
Chapter 4 argued that friction in a fluid is the loss of memory of an object’s initial, ordered
motion. The object’s organized kinetic energy passes into the disorganized kinetic energy of the
surrounding fluid. The world loses some order as the object merges into the surrounding distribution
of velocities. The object doesn’t stop moving, nor does its velocity stop changing (it changes with
every molecular collision). What stops changing is theprobability distributionof the particle’s many
velocities over time.
Actually, friction is just one of several dissipative processes relevant to living cells that we’ve
encountered: All obey similar Fick-type laws and all tend toerase order.Weneed to bring them all
into a common framework, the “Second Law” of thermodynamics introduced in Section 1.2.1. As
the name implies, the Second Law has a universality that goes far beyond the concrete situations
we’ve studied so far; it’s a powerful way of organizing our understanding of many different things.
Tomake the formulas as simple as possible we’ll continue to study ideal gases for a while. This
may seem like a detour, but the lessons we draw will be applicable to all sorts of systems. For
example, the Mass Action rule governing many chemical reactions will turn out to be based on the
same physics underlying the ideal gas (Chapter 8). Moreover, Chapter 7 will show that the ideal
gas law itself is literally applicable to a situation of direct biological significance, namely osmotic
pressure.
The goal of this chapter is to state the Second Law, and with it the crucial concept of free
energy. The discussion here is far from the whole story. Even so, this chapter will be bristling with
formulas. So it’s especially important towork throughthis chapter instead of just reading it.
The Focus Question for this chapter is:

©c2000 Philip C. Nelson

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