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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2013
    • (edited Nov 28th 2013)

    created a brief entry rational thermodynamics.

    I haven’t actually seen yet the actual detail of this axiomatics (but see the citations given at the above link). What I currently care about is this historical fact, which I added to the Idea section:

    What is called rational thermodynamics is a proposal (Truesdell 72) to base the physics of irreversible thermodynamics on a system of axioms and derive the theory from these formally.

    The success of the axioms of rational thermodynamics as a theory of physical phenomena has been subject of debate. But the idea as such that continuum physics can be and should be given a clear axiomatic foundation seems to have inspired William Lawvere (see there for more), once an undergraduate student of Clifford Truesdell, to base continuum mechanics on constructions in topos theory, such as synthetic differential geometry and cohesion.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 28th 2013

    I wonder if there’s useful material in Lawvere’s 16 page introduction to Categories in Continuum Physics, Lectures given at a Workshop held at SUNY, Buffalo 1982, Lecture Notes in Mathematics 1174, 1986.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2013

    Not in the introduction, I think, but now that I look again (thanks) I suppose the contribution by Coleman and Owen is about this. They don’t seem to say “rational thermodynamics” explicitly, but their text is about axiomatic irreversible thermodynamics and a footnote says that it later appared in an appendix to Truesdell’s book.

    (By the way, I had given this an nLab entry Categories in Continuum Physics)