6.1 The Project of Classical Formalism
The treatment in Chaps. 4 and 5 will be referred to as the Carnot and CKP
(Clausius, Kelvin, and Planck [1])
1 tradition. Born [2] spoke for all physicists who
subscribe to scientism
2 and reductionism when he wrote that the use of “the conception of idealized thermal machines” by Carnot and the CKP tradition for the
formulation of the second law of thermodynamics and the establishment of the
concepts of entropy and absolute temperature “deviated too much from the ordinary
methods of physics”—the methods of mechanistic physics which came down from
Galileo and Newton. (The prevailing view is that the doctrine of mechanism survived the challenge from the science of heat unscathed and, in fact, rose triumphantly with the rise of atomism but in the twentieth century faced and remains
facing the new, stronger challenge from the quantum revolution.) At Born’s suggestion, Carathéodory [3] developed an alternative formulation of the second law,
the classical formalism, which made no use of reversible “idealized thermal
machines” in the Carnot and CKP tradition. That is what Carathéodory, Born, and
generations of physicists since thought: the project of classical formalism succeeded
in removing reversible machines from the formulation of thermodynamic theory by
transforming the science of heat into a typical theory of mechanistic physics, which
is based on causal laws, e.g., the typical laws of physics such as Maxwell’s
equations, the heat transfer equation with Fourier’s law of heat conduction, the
Navier–Stokes equations, etc.
There are two problems with this view. First, the first law and the second law of
thermodynamics are not causal laws [4]. That is, they are not associated with
governing equations such as the Maxwell equations and Navier–Stokes equations,
and we shall study the implications of this point in Chaps. 8 and 10. The second
problem is one that is argued here: the formulation of Carathéodory’s principle (the
project of classical formalism) did not succeed in removing reversibility. Reversibility and the idea of machine or design, even if they do not appear explicitly,
are tacitly included in the classical formalism (see Sect. 6.3). Without them, we are
not certain why we can apply the doctrine of latent and sensible heats and why we
can use mathematical expressions such as the quasi-static work by Eq. (81), the
validity of which is taken, mistakenly, for granted in the classical formalism.
Let us first grant the rationale of the classical formalism that it is possible to
study a system in and of itself without having to refer to a reversible machine or/and
a reservoir. The formalism did give rise to Gibbsian thermodynamics. That was
indeed an extraordinarily successful first step. The conventional view is that
1
Uffink famously in Ref. [1] made this characterization of CKP, “the unargued statements of
Kelvin, the bold claims of Clausius and the strained attempts of Planck.” While CKP may not be
perfect in their logic or elegance (there is an opinion that P’s logic is better than that of C and K),
their scientific judgment is superior in my mind to that of Caratheodory and Uffink. Certainly, their
scientific legacy supports this opinion.
2
I use the term here somewhat like reductionism to mean the position that any concept that is not in
the governing equations of physics such as purpose, action, or the operation of thermal machines
has no scientific meaning.
136
6 Reversible Processes Versus Quasi-static Processes …
The treatment in Chaps. 4 and 5 will be referred to as the Carnot and CKP
(Clausius, Kelvin, and Planck [1])
1 tradition. Born [2] spoke for all physicists who
subscribe to scientism
2 and reductionism when he wrote that the use of “the conception of idealized thermal machines” by Carnot and the CKP tradition for the
formulation of the second law of thermodynamics and the establishment of the
concepts of entropy and absolute temperature “deviated too much from the ordinary
methods of physics”—the methods of mechanistic physics which came down from
Galileo and Newton. (The prevailing view is that the doctrine of mechanism survived the challenge from the science of heat unscathed and, in fact, rose triumphantly with the rise of atomism but in the twentieth century faced and remains
facing the new, stronger challenge from the quantum revolution.) At Born’s suggestion, Carathéodory [3] developed an alternative formulation of the second law,
the classical formalism, which made no use of reversible “idealized thermal
machines” in the Carnot and CKP tradition. That is what Carathéodory, Born, and
generations of physicists since thought: the project of classical formalism succeeded
in removing reversible machines from the formulation of thermodynamic theory by
transforming the science of heat into a typical theory of mechanistic physics, which
is based on causal laws, e.g., the typical laws of physics such as Maxwell’s
equations, the heat transfer equation with Fourier’s law of heat conduction, the
Navier–Stokes equations, etc.
There are two problems with this view. First, the first law and the second law of
thermodynamics are not causal laws [4]. That is, they are not associated with
governing equations such as the Maxwell equations and Navier–Stokes equations,
and we shall study the implications of this point in Chaps. 8 and 10. The second
problem is one that is argued here: the formulation of Carathéodory’s principle (the
project of classical formalism) did not succeed in removing reversibility. Reversibility and the idea of machine or design, even if they do not appear explicitly,
are tacitly included in the classical formalism (see Sect. 6.3). Without them, we are
not certain why we can apply the doctrine of latent and sensible heats and why we
can use mathematical expressions such as the quasi-static work by Eq. (81), the
validity of which is taken, mistakenly, for granted in the classical formalism.
Let us first grant the rationale of the classical formalism that it is possible to
study a system in and of itself without having to refer to a reversible machine or/and
a reservoir. The formalism did give rise to Gibbsian thermodynamics. That was
indeed an extraordinarily successful first step. The conventional view is that
1
Uffink famously in Ref. [1] made this characterization of CKP, “the unargued statements of
Kelvin, the bold claims of Clausius and the strained attempts of Planck.” While CKP may not be
perfect in their logic or elegance (there is an opinion that P’s logic is better than that of C and K),
their scientific judgment is superior in my mind to that of Caratheodory and Uffink. Certainly, their
scientific legacy supports this opinion.
2
I use the term here somewhat like reductionism to mean the position that any concept that is not in
the governing equations of physics such as purpose, action, or the operation of thermal machines
has no scientific meaning.
136
6 Reversible Processes Versus Quasi-static Processes …