Truesdell championed an axiomatic approach to continuum physics/irreversible thermodynamics which goes by the name “rational thermodynamics”. Exposure to this axiomatic approach partly motivated the development of synthetic differential geometry and cohesion by his student William Lawvere (see there for more) as a foundations for continuum mechanics.
Rational thermodynamics, Springer-Verlag, Berlin and New York, 1972
A first course in rational continuum mechanics. Pure and Applied Mathematics, Academic Press, New York, San Francisco, London, 1977, xxiii + 280 pp., $23.00 (review)
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