7. Applicability Limits of the Concept of Entropy.
These time intervals, though enormously great, are yet
finite and cannot therefore be ignored in cosmological
considerations. In applying the notion of entropy to
the universe at large, Boltzmann, following a sugges-
tion made by his long-time assistant L. Schuetz, de-
scribed the universe as follows: though generally in
thermal equilibrium “and therefore dead,” it contains
“here and there small regions of the same size as our
galaxy which, during the relative short time of eons,
fluctuate noticeably from thermal equilibrium” and in
which the entropy “will be equally likely to increase
or decrease” (Boltzmann, 1896-98). In recent years the
applicability of the entropy concept to such cosmolog-
ical considerations has been repeatedly questioned
(Plotkin, 1950; Milne, 1952). Whether the introduction
of an upper boundary to the applicability of the
entropy concept—like that of its lower boundary
(Maxwell's demon)—will eventually be refuted remains
an open question.
Nor has a unanimous answer been obtained to the
problem whether the notion of entropy fully applies
also to biology. Helmholtz had envisaged the possibility
of cytological processes being associated with entropy
decrease, a thesis which subsequently was given limited
support by H. Zwaardemaker, but rejected by the
majority of contemporary biologists. It gained a revival
of interest when in 1910 Felix Auerbach, an ardent
proponent of biological entropy decrease, adopted
from G. Hirth (Hirth, 1900) the notion of “ectropy”
as the biological antithesis of entropy, and promulgated
this concept in his popular work
>Ektropismus oder die
physikalische Theorie des Lebens (Auerbach, 1910). The
issue is of course intimately connected with the conflict
between biological mechanism, according to which
biological phenomena can be exclusively explained in
physicochemical terms, and vitalism, according to
which the processes of life have a character
sui generis.
