I'm going to concentrate on the statistical mechanics side of the question here.
My first recommendation would be Introduction to Modern Statistical Mechanics by David Chandler (Oxford University Press, 1987). This book is not particularly long, but it covers a broad range of material, and is very well written. As well as reprising your knowledge of classical thermodynamics concisely, it introduces statistical ensembles in a clear way, and moves on from the standard "ideal" systems to systems of interacting particles. There is a chapter on phase transitions, and one on the statistical mechanics of non-equilibrium systems (which covers linear response theory, fluctuation-dissipation, and related things). So it seems like a good fit with what you want.
Secondly, I'm inclined to recommend Statistical mechanics: theory and molecular simulation by Mark Tuckerman (Oxford University press, 2010), but with some caveats. This is not a short book: it grew out of the lecture notes accompanying Tuckerman's graduate course(s), and is full of detail. A fair fraction of the book discusses molecular dynamics simulation methods, which are intimately connected to some of the statistical mechanics being discussed. For me this is a "plus" point, but perhaps it will not be so relevant to you. As well as the standard topics (ensembles, statistical mechanics of ideal systems, the Langevin equation, and a chapter on critical phenomena that basically scratches the surface) there are a few topics that are hard to find elsewhere. The connection between nonequilibrium statistical mechanics and the underlying hamiltonian and non-hamiltonian dynamical equations, is well explained here. He introduces the Jarzynski equality, which has had a big impact on our understanding of the relation between work and free energy in nonequilibrium processes (along with the Crooks fluctuation theorem, and other fluctuation theorems, which you may have to research elsewhere). He also gives a good account of Feynman's path integral formulation of quantum mechanics. So, a good book to dip into, and read the relevant sections.
Finally, I'm going to suggest taking a look at An Introduction to Statistical Mechanics and Thermodynamics by Robert Swendsen (Oxford University Press, 2012), again with some caveats. This is a refreshingly different account of some familiar topics in the area of statistical thermodynamics. The novelty comes from the starting point, in probability theory, entropy, and the molecular description. Mathematical techniques are introduced along the way, as needed. Some "standard" thermodynamics equations (such as Maxwell relations) don't appear until nearly half way through.
According to some reviews, there are a lot of typographical errors (I can't say that I've counted them),
so that's probably a "minus" point. The coverage of nonequilibrium phenomena probably falls short of what you need; there's almost nothing on dynamics. But it covers phase transitions very well, and in general it does give an interesting perspective.