2. A Modernized Version of the Thermodynamic
Definition of Entropy. With the extension of thermo-
dynamics at the end of the last century to electrical
and magnetic phenomena, to elastic processes, phase
changes, and chemical reactions—the result of re-
searches by J. W. Gibbs, Helmholtz, H. A. Lorentz,
P. Duhem, W. H. Nernst, and others—it was felt unsat-
isfactory that a science of such astounding generality,
and especially such central conceptions as that of
entropy, should be based on engineering experience
with heat engines and their cycles. L. J. Henderson's
critical remark, that “the steam engine did much more
for science than science ever did for the steam engine,”
served as a serious challenge for those concerned with
foundational research. Stimulated by Max Born, who
as a student had criticized the conventional approach
as deviating “too much from the ordinary methods of
physics” (Born, 1921), Constantin Carathéodory re-
placed this approach in 1908 by a purely axiomatic
treatment, based on the integrability properties of
Pfaffian differentials (Carathéodory, 1909). His “prin-
ciple of adiabatic unattainability”—according to which
adiabatically inaccessible equilibrium states exist in the
neighborhood of any equilibrium state, this being a
mathematical reformulation of the impossibility of a
perpetual motion of the second kind—implies the
existence of an integrating divisor only tempera-
ture-dependent and hence of the entropy S. Due to
the mathematical intricacies of Carathéodory's ideas,
they were generally ignored in spite of the enthusiastic
acceptance by Born, A. Landé, S. Chandrasekhar, and
H. A. Buchdahl. Since 1958, however, primarily after
having been simplified by L. A. Turner, F. W. Sears,
and P. T. Landsberg, Carathéodory's approach became
more popular, and his definition of entropy is now
presented even in textbooks of thermodynamics (P. T.
Landsberg, 1961; I. P. Bazarov, 1964).
