1) The pioneer of the rigorous treatment of thermodynamics is Constantin Carathéodory. His aticle (Carathéodory, C., Untersuchung über die Grundlagen der Thermodynamik, Math. Annalen
67, 355-386) is cited everywhere in this context, but probably you want some newer and more modern things.
2) Buchdahl wrote a lot of papers about this subject in the 40's, 50's and 60's. He summarized these in the book:
H.A. Buchdahl, The Concepts of Classical Thermodynamics (Cambridge Monographs on Physics), 1966.
3) There was a recent series of articles on this subject by Lieb and Yngavason which became famous. You can find the online version of these here, here, here and here :).
4) Finally, I have come across the book T. Matolcsi, "Ordinary Thermodynamics" (since a few friends of mine went to the class of the author), which treats thermodynamics in a mathematically very rigorous way.
I hope some of these will help you.
Greetings,
Zoltan
This post imported from StackExchange Physics at 2014-04-26 06:48 (UCT), posted by SE-user Zoltan Zimboras