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I have posted this question on StackExchange, but no one seems to care answer. Because I don't think this is a simple textbook question, I start my thread here:

I know this is a big question. But as a graduate student, my research is somehow related to nonequilibrium thermodynamics/statistical mechanics. TBH, I hate how some research treat this subject like a mystery and use some theories carelessly. So I want to learn the subject at my own pace. I have finished Fermi Enrico's "thermodynamics" for a start. And I'm reading Terrell Hill's "introduction to statistical thermodynamics." Although I am pretty satisfied with the content of these two books, I have no idea where should I go from here.

Because I expect my future research will still be based on nonequilibrium thermo/stat mech, I need a booklist to guide me from "knowing something" to "knowing something advanced." In the meantime, I hope I can equip myself with advanced mathematics by going through the booklist. Can anyone provide some ideas on this?

To be more precise, my research interests include the particle diffusion in crystal materials and phase transition. And I also expect to do some research in the future about the transport of heat and charged species in the liquid or solid phase.

P.S., I am not looking for working understanding of this subject. A solid but accessible booklist would be perfect.