Statistical mechanics by its plain definition is a broad field, but most introductory textbooks focus on its applications in thermodynamics. Are there introductory texts that take up a broader view of statistical mechanics? For instance, I am interested in being able to learn enough to answer questions of the following sort (random examples):
(many colliding balls) Given an initial condition in an idealized 2D random walk system (vacuum with randomly walking elastic balls) where all particles are packed at the centre, which function (exponential, $1/x^2$, etc.) will best describe the concentration of the particles (with respect to space) after some time, before equilibrium has been reached?
(many rigid rods) Given a 2D structural system composed of many microscopic rigid bodies where the "connection topology" of struts is uncertain (i.e. struts are not always connected to the same partners), what macroscopic stress-strain properties can we expect the system to have?
Additionally, I would prefer a book that is self-contained in terms of physics concepts beyond undergraduate classical mechanics, while being rigorous mathematically. So, its okay for the book to not be self-contained in terms of the mathematics required.
