8. The Boltzmann Problem. What may be called
“the Boltzmann problem,” namely the question as to
the minimum additional assumption, if any, necessary
to derive macroscopic irreversibility from pure me-
chanics, is also philosophically of great importance. On
the solution of this problem depends decisively whether
a purely mechanistic explanation of nonelectromag-
netic phenomena is possible. Until quite recently the
conceptual difficulties were usually overcome by the
introduction of probabilistic assumptions a priori, such
as Boltzmann's hypothesis of a molecular chaos in his
Stosszahlansatz. It was soon understood, however, that
these assumptions, though not inconsistent with the
principles of pure mechanics, are nevertheless not
derivable from them. A general tendency arose to
banish probability from statistical mechanics as far as
possible.
With the advent of quantum mechanics, which like
classical mechanics is time reversal invariant, it seemed
for some time, as shown in a paper published by W.
Pauli in 1928, that the above-mentioned probabilistic
hypotheses could be derived from the statistical aspects
inherent in the very foundations of the quantum theory.
A certain equation, derived on the basis of Dirac's
perturbation theory, which describes the transition
probabilities between quantum mechanical states,
appeared appropriate for the treatment of irreversible
processes. This so-called “master equation” (T. Prigo-
gine, P. Résibois) in conjunction with the Hermiticity
assumption of perturbation operators, made it possible
to derive all laws of thermodynamics as well as the
phenomenological equations for thermal conduction,
diffusion, and even the Onsager reciprocity relations,
without major difficulties (R. T. Cox, 1950, 1952;
E. C. G. Stueckelberg, 1952; J. S. Thomsen, 1953; N. C.
van Kampen, 1954).
Since 1958, however, the logical legitimacy of using
perturbation theory in this context has been seriously
questioned, and new attempts to solve this problem
were made in the so-called “thermodynamics of irre-
versible processes.” In 1968 it became apparent that
irreversibility is intimately connected with the coexist-
ence of phases in equilibrium and occurs whenever a
thermodynamic variable is coupled through an equi-
librium process to another independent variable. (See
D. G. Schweitzer, “The Origin of Irreversibility from
Conventional Equilibrium Concepts,” Physics Letters
27a [1968], 402-04.)
Contemporary investigations of the “Boltzmann
problem” are very important also for foundational
research on quantum mechanics and, especially, on its
theory of measurement, since here quantal phenomena
are coupled with macroscopic irreversible processes
that occur in the measuring device (G. Ludwig, P.
Bocchieri, A. Loinger, G. M. Prospèri). Also Louis de
Broglie's (1964) reinterpretation of quantum mechanics
as a hidden thermodynamics (thermodynamique cachée
des particules) will be greatly affected by the outcome
of these investigations.
