Mechanics Book For Bsc Physics
Lilliana Adames
The principles of mechanics successfully described many other phenomena encountered in the world. Conservation laws involving energy, momentum and angular momentum provided a second parallel approach to solving many of the same problems. In this course, we will investigate both approaches: Force and conservation laws.
Our goal is to develop a conceptual understanding of the core concepts, a familiarity with the experimental verification of our theoretical laws, and an ability to apply the theoretical framework to describe and predict the motions of bodies.
The more math I read, the more I see concepts from statistical mechanics popping up -- all over the place in combinatorics and dynamical systems, but also in geometric situations. So naturally I've been trying to get a grasp on statistical mechanics for a while, but I haven't been very successful. I've skimmed through a couple of textbooks, but they tended to be heavy on the physical consequences and light on the mathematical underpinnings (and even to an extent light on the physical/mathematical intuition, which is inexcusable!)
I suspect that part of the problem is that, unlike the analogous situation with quantum mechanics, I'm not sure what mathematics I can fall back on if I don't "get" some statistical model. So, is there a good resource for statistical mechanics for the mathematically-minded?
A classic book on solvable two-dimensional models is Baxter's "Exactly Solved Models in Statistical Mechanics" now available in a new edition from Dover. The Yang-Baxter equation, of course, has many connections with important branches of mathematics. This book explains its origins and use in solving certain physically motivated models.
If you are looking for a book, the real answer is "not really". As a mathematician masquerading as a physicist (more often than not of a statistical-physical flavor) I have looked long, hard, and often for such a thing. The books cited above are some of the best for what you want (I own or have read at least parts of many of them), but I would not say that any are really good for your purposes.
Many bemoan the lack of The Great Statistical Physics text (and many cite Landau and Lifshitz, or Feynman, or a few other standard references while wishing there was something better), and when it comes to mathematical versions people naturally look to Ruelle. But I would agree that the Minlos book (which I own) is better for an introduction than Ruelle (which I have looked at, but never wanted to buy).
Other useful books not mentioned above are Thompson's Mathematical Statistical Mechanics, Yeomans' Statistical Mechanics of Phase Transitions and Goldenfeld's Lectures On Phase Transitions And The Renormalization Group. None of them are really special, though if I had to recommend one book to you it would be one of these or maybe Minlos.
You might do better in relative terms with quantum statistical mechanics, where some operator algebraists have made some respectable stabs at mathematical treatments that still convey physics. But really that stuff is at a pretty high level (and deriving the KMS condition from the Gibbs postulate in the Heisenberg picture can be done in a few lines) so the benefit is probably marginal at best.
It sounds like your goal is primarily to get a quick overview of how mathematicians use statistical physics, with lots of intuition, and lots of applications to nearby areas, but not necessarily much physics or any 'best possible' results. If that is the case, the Montanari/Mezard book `Information, Physics and Computation' is excellent. The emphasis is on teaching many different techniques, rather than on the statistical physics itself, and it is really written as a textbook rather than a reference book (i.e. the theorems are the easiest ones to understand, not the most powerful ones to use). In other words, it has exactly the mathematical underpinnings, but doesn't cover what many of the other books treat as central material.
We have finished writing an introductory book on (some aspects of) equilibrium statistical mechanics, with mathematicians (and mathematically-inclined physicists) in mind. A draft of the version of the complete book, as it was sent to its publisher (Cambridge University Press), can be downloaded from this page. It should more or less coincide with the final version (modulo corrections that will be made on the galley proofs), that we hope will be published mid-2017.
"Statistical Mechanics: Entropy, Order Parameters, and Complexity" by James Sethna (my favorite) and "Statistical Mechanics" by Kerson Huang are both really good books. Sethna's book is very readable and engaging; Huang's is more of a syatematic textbook.
Ruelle's book is mathematically rigorous but is aimed at people who already know something about the field. Baxter's book is incredibly valuable for what it covers, but it is highly specialized and provides no motivation for people who aren't already comfortable with the basic formalism.
And, there are many surveys and currently appears new reviews about some topics, some examples(I included pages of mathematicians that work on the subject, in their pages you can get some introductory texts):
There are apparently only a few books on rigorous results in statistical mechanics. David Ruelle's books are apparently standard, though I found them difficult to digest when I picked them up. One which I found more accessible is "Introduction to Mathematical Statistical Physics" by Minlos.
A personal note is that I found statistical mechanics very unintuitive and difficult to learn at first. I felt that the formalism didn't come together for me until I was familiar with a multitude of physical systems.
Two other books which are worthwhile I find R.B. Israel: Convexity in the Theory of Lattice gases. It has wonderful introduction by Wightman , which is like book in itself. it is limited in scope but is excellent in what it treats.T.C. Dorlas Statistical mechanics, is written by a mathematical physicist and covers many topics in a more rigorous way than most physics textbooks do.
It's certainly not a basic book, but Itzykson and Drouffe's "Statistical Field Theory" gives a good overview of the use of quantum field theory techniques in statistical mechanics. Some of the chapters are quite readable.
Start here: An Introduction to Thermal Physics by Dan Schroeder is an excellent introduction that provides a single, consistent mathematical underpinning providing the insight necessary to truly understand things like entropy and the differences between the classical and quantum cases of statistical mechanics. I can't emphasize enough how important the core ideas of that book are to understanding the foundations of statistical mechanics. (As an aside, Schroeder also happens to be the coauthor, with Michael Peskin, of An Introduction to Quantum Field Theory which has purportedly replaced Bjorken and Drell as the standard in that field, though this is only hearsay.)
This topic is old, but I'll still add my 2. I usually don't really like statistical mechanics books aimed at physicists, as they are often much more focused on computational techniques than on concepts. There are however very good lecture notes by Yoshi Oono, available on his page:
This book is aimed at physicists, but contains a very unusual amount of mathematical content, esp. in footnotes, with many references to the math. phys. literature. This book assumes that the reader already has some knowledge of this field. There are other lecture notes, aimed at undergraduates, on his page as well (I haven't looked closely at those, so I cannot comment on their quality):
Maybe I didn't read the replies well enough, but apparently no one mentions A. Khinchin's book Mathematical Foundations of Statistical Mechanics. I just started reading this book. It's definitely mathematical and specifically says that it's written for a mathematician. The notation is a bit old, but the book is very readable, and far, far better than any book of physics I've seen lately.
A really good first textbook for statistical mechanics is David Chandler's Introduction to Modern Statistical Mechanics. It's written by a physical chemist for senior undergraduates and does an excellent job distilling down the very fundamental material into a one-semester course at Berkeley. It's not at all math heavy.
Two short easy places to start. Of course after that, there are lots.Schroedinger's lecture notes on Statistical Thermodynamics are a clearly thought out gem of pedagogy, it was really his forte. And you don't need to finish the book either.
Statistical Mechanics of Disordered Systems, a Mathematical Perspective, by Anton Bovier. Part I provides a brief introduction to statistical mechanics, while the rest two parts focus on disordered systems. To my understanding, the author treats the problems from a mathematical point of view.
I've only briefly looked at it but the book Statistical Physics of Particles by Mehran Kardar seems pretty good. It starts with an introduction to the relevant probability theory and then moves on to the basics of statistical mechanics. There is also a subsequent book Statistical Physics of Fields.
Mechanics (from Ancient Greek: μηχανική, mēkhanikḗ, lit. "of machines")[1][2] is the area of physics concerned with the relationships between force, matter, and motion among physical objects.[3] Forces applied to objects result in displacements, which are changes of an object's position relative to its environment.
Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes[4][5][6] (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics.
As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm.
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