Although statistical mechanics and thermodynamics have separate historical roots, they are very closely related. The founders of thermodynamics developed their theory without modern understanding of the atomic structure of matter. Statistical mechanics builds on this understanding and makes predictions about system behavior that lead to thermodynamic laws. In other words, statistical mechanics is a conceptual forerunner of thermodynamics, albeit a historical latecomer.

Unfortunately, however, statistical mechanics and thermodynamics are often taught as separate fields of study, despite their theoretical connections. Worse, thermodynamics is usually taught first on the dubious grounds that it is older than statistical mechanics. As a result, students too of ten view thermodynamics as a very abstract set of mathematical relationships, the significance of which is not clear.

**About the Book**

The hypothetical approach to thermodynamics is based primarily on the work of László Tissa, who was his and his thesis advisor, and provides a clear foundation for the theory. The theory is not difficult to understand, but may seem rather abstract when first encountered as a student. Many professors have said that they found Cullen’s book too daunting to teach to their students, but that they referred to it when studying thermodynamics.

The first part of this book began as an introduction to Cullen’s Thermodynamics, which was used in my teaching. The difficulty I had as a student was that Cullen’s book introduced entropy and thermodynamic theorems inChapter1 and temperature as the partial derivative of entropy in Chapter2.

Part II evolved from my notes for teaching Cullen’s textbook. Although the idea of Cullen’s theorem is an excellent foundation for thermodynamics, I found that its specific form is not ideal. In the first edition of this book, I divided the theorem in to six new theorems, each expressing an independent idea. We also generalized the theorems to include non homogeneous systems. I gave clear guidance on the use of the Jacobian in the derivation of thermodynamic identities. Cullen mentioned the Jacobian in the first edition, but not in the second edition.

In Parts III (classical statistical mechanics) and IV (quantum statistical mechanics), we made extensive use of computer calculations. This allowed me toper form many calculations explicitly.