NB. I was sent this book as a review copy.

From Princeton University Press

I am in two minds about this book. On the one hand, I hugely enjoyed it and it IS an incredible overview of the many beautiful facets and uses of information theory, from classical thermodynamics to the PageRank algorithm to Quantum Information theory and beyond. I thought that it dealt with entropy more clearly and interestingly than I’ve seen in any other textbook. The writing is at times poetic and at others very careful, and as such it was a pleasure to read it. On the other hand it is a 150 page (plus appendices) book, that covers wide, and complex ground and, in the preface states that “This book is an introduction that requires prior knowledge of neither thermodynamics and statistics nor information theory.” It is said that “The textbook is self-sufficient and contains no reference list.” However, I fear that both of these statements just aren’t quite correct. Section 1.1 dives into the basics of thermodynamics and in the second paragraph introduces Carnot’s famous inequality, putting limits on the heat transfer from a hot to a cold reservoir, and with that, entropy is introduced. It’s always hard to put yourself into the mind of someone who has not studied what you have, and so I’m really having to do a bit of educational gymnastics, but I think that if I hadn’t previously studied thermodynamics, the first ten pages of the book (and thus what follows) which introduces most of classical thermodynamics, would have been very hard to follow.

That being said, having studied this in the past, his survey of the topic is wonderfully written, and it did make me rethink my understanding of the ideas, making me realise many points that I had not valued when I learned them the first time. However, 16 pages isn’t, I think, enough to introduce, and conclude a chapter on thermodynamics in all its mathematical detail.

This all comes with an additional caveat, which I think saves the book for me, and that is that, with an instructor and a lot of gaps filled in, this chapter would form the basis of a very interesting first course in thermodynamics. I think that the same could be said for chapter 2, which is a 30 page overview of information theory, which again, with an instructor and a lot of additional detail, would give a very intuitive overview of the subject once the details have been given.

Overall, the topics chosen for the book are fascinating, covering applications of information theory, non-equilibrium thermodynamics, irreversibility, and finally the impact of quantum mechanics on uncertainty, including black hole thermodynamics. Covering all of this in 140 pages inevitably means that a lot is covered very quickly, and as such I would not recommend this book as a standalone book for the average undergraduate. However, a really keen undergraduate would be able to take a chapter, and use it as part of a curriculum to learn each topic, or, as stated above, an instructor could take a chapter or two and make a very nice course out of it, with appropriate cognitive padding and exercises.

Information theory is a topic which is often neglected in an undergraduate physics degree. Not that it is not included, but that its significance is often not made clear, and yet this book shows quite how fundamental it is to so many fields, and that we often fail to grasp its deeper meaning and how much it can actually give to our overall understanding of the universe at every scale.

I think that the book itself is wonderful, I just worry a little that the preface sets Falkovich up for failure if his intentions are to have a self-contained, accessible text for all-comers. If you don’t read it as such though, I think that you are likely to enjoy it a lot.