Elementary Principles in Statistical Mechanics

The themes of thermodynamic connections to statistical mechanics had been explored in the preceding decades with Clausius, Maxwell, and Boltzmann, together writing thousands of pages on this topic.

At the time of the book's writing, the prevailing understanding of nature was purely in classical terms: Quantum mechanics had not yet been conceived, and even basic facts taken for granted today (such as the existence of atoms) were still contested among scientists.

In this, he introduced the now standard concept of ‘ensemble’, which is a collection of a large number of indistinguishable replicas of the system under consideration, which interact with each other, but which are isolated from the rest of the universe.

Thus, the ensemble averaging method provides us an easy way to calculate the thermodynamic properties of the system, without having to observe it for long periods of time.

Even today, the concept of ensemble is widely used for sampling in computer simulations of the thermodynamic properties of materials, and has subsequently found uses in other fields such as quantum theory.