Statistical mechanics is used in thermodynamics. Statistics and probability theory forms a large part of the basis for quantum mechanics. Bose-Einstein statistics have particular applications in quantum thermodynamics, laser beams and quantum descriptions of matter near absolute zero.
Statistical mechanics is a branch of physics used mainly to extract global properties of a system while accounting for most (if not all) contributions from its constituents in some approximated manner.
i.e. You can use statistical mechanics to calculate the energy of a paramagnet while accounting for all the values that each individual molecule's energy can be.
Statistical physics is the coolest field of physics. Well, to me at least. So what is it? Sentin3l's description above is quite good. Often the idea is indeed that given the microscopic interactions between particles, you want to extract some macroscopic properties. Say, for example that you have a bunch of charged particles, so you know that the force between them follows Coulomb's law, and you want to know what kind of pressure they exert if you put them into a box. Or you would like to know the structure factors (something you can obtain by x-ray experiments). Or you want to know at which temperature the material has phase transitions from gas to fluid to solid. You would use tools from statistical physics.
Now two things make statistical physics supercool. First is its mathematical nature: If you like doing maths, there are few areas in physics where it really gets more intense (tellingly, much of statistical physics is actually done by mathematicians or mathematical physicists). On the other hand you can understand the concepts and formulate new models without going into the hard core stuff. Once you fully understand the Ising model, you can in a simplistic way formulate anything in that formalism.
Statistical physics is really fundamental, and you can derive relations that apply to all of matter. Perhaps owing to the mathematical nature and the fact that generating new models is in principle easy, new fundamental relations are still being discovered: Classical physics is not "complete" yet. For example the Jarzynski equality is only some 20 years old and is now part of any comprehensive introduction to statistical mechanics book.
The second cool thing? It is applicable outside physics. You might have heard the terms sociophysics or econophysics. These are rapidly growing fields in which physicists use their knowledge of physics to problems in sociology and economics. What kind of physics knowledge exactly? More often than not, you guessed it, statistical physics. As I said, model formulation in statistical physics is very easy: you come up with a model how on the microscopic scale things work, for example you propose that securities dealers tend to imitate one another to a certain degree, and then you solve for what it means for some macroscopic quantities, say how exactly this imitation can lead to stock market crashes and how one can see them coming by looking at some macroscopic quantities.
This is how I would describe statistical physics and I think it's fun.
Sounds like an interesting branch from the replies. Could your recommend any good introductory books on the subject? I haven't had too much crazy math yet just up to calculus and about to start linear algebra. I don't know if anyone has read this book, but I found a copy of Thermodynamics and Statistical Mechanics by W. Greiner, L. Neise, H. Stocker online. It seems to use a decent level of mathematics.
Are you more interested in statistical physics or thermo?
Either way I would NOT recommend Kerson Huang's book.
I would recommend going to the nearest University library and looking through all the books on intro stat phys and reading a bit from all of them and looking for the one that has a writing style that speaks to you and has practice problems.
In nearly all of physics you need an application. This is what separates physics from mathematics and makes the former a natural science, while the latter is more akin to philosophy, and not necessarily rooted in the real world. Now you have done classical physics where everything is in the end based on Newton's equations of motion. Given this framework, you take an application, say Tarzan's trajectory as he attempts to swing across a river, and try to figure out what happens.
Statistical physics is a huge subject and it applies to any system which is made up of a large number of smaller parts interacting with each other. It is therefore important that you try to figure out more specifically what you are interested in: You wouldn't want to waste too much of your time reading up on quantum statistics if what you really are interested in is describing the liquid state.
Here are couple of the more recent books, starting from very basic and going up to intermediate stuff:
"An Introduction to Thermal Physics" by Daniel V. Schroeder. This is a rather standard book for a first course on thermodynamics and statistical mechanics. Most of the book is focused on the former, and the latter is introduced through the partition function basics using an Ising model and an elementary discussion about fermions and bosons and their associated statistics. I don't think the book contains anything that you don't need to know, it is fairly application-field agnostic, and from what I remember, the exposition is very clear and everything is made very simple. You will learn what free energy is and how it connects to the partition function.
"Statistical Mechanics: Theory and Molecular Simulation" by Mark E. Tuckerman. This is a recent book that I have not fully read, but I have read chunks of. The exposition is excellent and the connection to molecular simulations is kept very clear. Not the book you might necessarily want if you want to do liquid state DFT, but if you want a comprehensive understanding of how molecules interact and how statistical mechanics arises from those interactions (mainly classical, but also a chapter or two on quantum stuff), I know of few books that I rate higher than this one. This book starts with a thorough review of classical mechanics, thermodynamics and statistical mechanics and goes on to describe some relatively recent advances and how they are actually used in practice in simulations.
Finally, if I recall correctly Coursera/edX and other MOOC sites have recently had courses on introductory statistical mechanics. You might want to look into those venues as well.
To close, "Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more" -- Arnold Sommerfeld, one of the leading minds of his time. I can fully attest to this quote, and I often go from thinking that I comprehend thermodynamics to the realization that even when my models and equations work, I do not fully at a fundamental level understand why.