Classical thermodynamics is developed in a rigorous and quite general form. The approach is similar to Carathéodory's in that entropy and temperature are defined in terms of quantities which are more directly measurable, but Pfaffian forms and quasistatic processes do not appear. The mathematics used is elementary, apart from a small amount of symbolic logic and a very little topology.

1.
C.
Carathéodory
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Math. Ann.
67
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355
(
1909
);
C.
Carathéodory
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Sitzber. Preuss. Akad. Wiss. Physik‐Math. Kl.
39
, (
1925
).
2.
An extended version of the Carathéodory theory is given in P. T. Landsberg, Thermodynamics (Interscience, New York, 1961).
3.
H. A.
Buchdahl
,
Z. Phys.
168
,
316
(
1962
).
4.
R. Giles, Mathematical Foundations of Thermodynamics (Pergamon, Oxford, 1964).
5.
G. Falk and H. Jung, Handbuch der Physik III/2 (Springer, Berlin, 1959).
6.
H. A.
Buchdahl
and
W.
Greve
,
Z. Phys.
168
,
386
(
1962
).
7.
E. A. Guggenheim, Thermodynamics (North‐Holland, Amsterdam, 1957), 3rd ed.
8.
H. B. Callen, Thermodynamics (Wiley, New York, 1960).
9.
L. Tisza, Generalized Thermodynamics (M.I.T. Press, Cambridge, Mass., 1966).
10.
One could say macroscopic state, but we will be concerned with no other kind.
11.
It is to ensure this uniqueness that we introduce the coordinates xi with i>l,i∉I. Consider, for example, a system that consists of a solid block. A given amount of heat absorbed in a process might warm the whole block without changing its phase, or it might melt a corner off. By including among the coordinates some that determine the geometry of the block, we can specify which of these alternatives is to occur in an anergic process.
12.
A similar restriction on anergic processes is implicit in Axiom X of the formal theory.
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