home | literature reviews

## "Statistical mechanics: Rigorous results", David Ruelle, 1969

*Reviewed January 28, 2024*

*Citation:* Ruelle, David. Statistical mechanics: Rigorous results. 1969.

*Web:* https://www.worldscientific.com/worldscibooks/10.1142/4090#t=aboutBook

*Tags:* Physical, Statistical-mechanics

This book is David Ruelle's treatise on rigorous mathematical results in statistical mechanics.
This book is focused on general principles, and is well-complimented by Baxter's book on exactly solved models:

> Baxter, Rodney J. Exactly solved models in statistical mechanics. Elsevier, 2016.

An aspect of particular note in this book is the preface, where David Ruelle makes a case
for what mathematical physics can be. Seeing as this book is not freely available on the internet, I
take the liberty to quote the core of this preface below:

"Physics is a human attempt at understanding a certain class of natural phenomena, using scientific methods.
We shall not try to define scientific methods in general, but note that they have been very successful and very diverse.
Mathematical physics is one of these methods or approaches in which a mathematical structure is somehow associated
with the structure of the physical phenomena. The mathematical structure is then studied by mathematical techniques to yield
new statements with physical relevance. Provided it yields physically relevant statements, no mathematical technique is
to be judged too sophisticated or too trivial.

Applying the tools of mathematics to the investigation of the physical world may be a very rewarding intellectual experience.
On the one hand, the knowledge which we have of physical hints at new mathematical theorems and at ways of proving them.
On the other hand, mathematical analysis gives to the physical world a new structure and meaning. The knowledge of this
structure and meaning constitutes an understanding of the "nature of things" as deep as we can hope to be.

Not every field of physics yields interesting mathematical physics. Luckily, we live in a period
with many unsolved problems that are interesting and appear amenable to treatment. An exception
to this statement may be relativistic quantum mechanics, largely because of "overgrazing", but
there are vast areas of *terra incognita*."