5.1 Introduction

Most physical, chemical and biological systems (gases, liquids, solids, radiation, plasmas) consist of a very large number of particles, typically of order \(N_A\sim10^{23}\). In principle one could write down the equations of motion for every particle. In practice the complexity is so great that useful results are almost impossible to obtain that way.

Yet it is precisely this complexity that makes a statistical treatment possible. When the number of particles is enormous, averages become extremely sharp, and macroscopic properties can be predicted with great precision from the laws of probability. The aims are to use the basic laws of physics to develop concepts that bring out the essential features of complex systems, and to recognise important relationships and make useful predictions.

Microscopic and macroscopic systems. A system is microscopic if it is of atomic dimensions or smaller (≲ 10 Å), for example a molecule. It is macroscopic if it is large enough to be seen in the ordinary sense (≳ 1 μm), and then it contains very many atoms.

Macroscopic parameters are quantities such as volume, pressure, magnetic moment, thermal conductivity, temperature, heat and entropy.

Equilibrium. If the macroscopic parameters of an isolated system do not change with time, the system is in equilibrium.

Four approaches