2 - Statistical entropy

Summary

Boltzmann and atoms

The thermodynamic view of a physical system is the “black box” view. We monitor the input and output of a black box and measure its superficial characteristics with the human-sized instruments available to us: pressure gauges, thermometers, and meter sticks. The laws of thermodynamics govern the relations among these measurements. For instance, the zeroth law of thermodynamics requires that two black boxes each in thermal equilibrium with a third are in thermal equilibrium with each other, the first law that the energy of an isolated black box can never change, and the second law that the entropy of an isolated black box can never decrease. According to these laws and these measurements each black box has an entropy function S(E,V, …) whose dependence on a small set of variables encapsulates all that can be known of the black box system.

But we are not satisfied with black boxes – especially when they work well! We want to look inside a black box and see what makes it work. Yet when we first look into the black box of a thermodynamic system we see even more thermodynamic systems. A building, for instance, is a thermodynamic system. But so also is each room in the building, each cabinet in each room, and each drawer in each cabinet. But actual thermodynamic systems cannot be subdivided indefinitely. At some point the concepts and methods of thermodynamics cease to apply. Eventually the subdivisions of a thermodynamic system cease to be smaller thermodynamic systems and instead become groups of atoms and molecules.