nLab rational thermodynamics

Idea

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.

References

Original books include

• Clifford Truesdell, Rational thermodynamics, Springer-Verlag, Berlin and New York, 1972

• Clifford Truesdell, A first course in rational continuum mechanics. Pure and Applied Mathematics, Academic Press, New York, San Francisco, London, 1977, xxiii + 280 pp., (review)

The appendix of (Truesdell 72) also appears as

• Bernard Coleman, David Owen, Recent research on the foundations of thermodynamics, in William Lawvere, Stephen Schanuel (eds.), Categories in Continuum Physics, Lectures given at a Workshop held at SUNY, Buffalo 1982. Lecture Notes in Mathematics 1174 1986

A survey of approaches to irreversible thermodynamics is in

• Ivan Vavruch, Conceptual problems of modern irreversible thermodynamics, Chem. Listy 96 (2002) (pdf)

with a review of rational thermodynamics in section 3.