Re: Second law of Thermodynamics

Don N Page (
Tue, 18 Nov 97 15:59:15 -0700

Jan de Koning wrote Tue, 18 Nov 1997 15:11:22 -0500, "Not everyone
agrees with this law [the second law of thermodynamics]. I am not a physicist
but as far as I know it only holds for closd sytems. It has not been show to
be true for open systems."

I think virtually all physicists would agree that the second law is, to
at least some high degree of approximation, almost always true within our
universe. In the further approximation that one can localize entropy into
separate subsystems (so that the total entropy of the entire universe, the
smallest thermodynamically closed system containing us, can be approximated by
the sum of the entropies of the subsystems) and that one can measure the
entropy flow into or out of each subsystem by the heat flow (divided by the
absolute temperature) into or out of each subsystem, then one can state a
second law for each open subsystem: the entropy generated within each
subsystem (the increase plus the outflow minus the inflow) is never negative.
This is also quite widely true, to a very high degree of approximation, though
it can be invalidated by quantum interference and/or other similar effects
between certain subsystems sufficiently correlated and simple that their
entropies are not additive (i.e., their joint entropy is not the sum of their
separate entropies).

The general approximate truth of the second law, even for almost all
macroscopic open systems, is not strongly doubted, but difficulties arise when
one seeks an absolutely precise formulation of the second law that would always
be valid (difficult because the very concept of entropy seems to depend upon
some sort of coarse-graining that is very hard to objectify and make precise),
or when one seeks to give an explanation of the second law. It seems that the
second law cannot be derived from the basic dynamical laws of physics (which do
not have any known preference for the future over the past, except to a very
tiny degree relative to the arbitrary choice of which particles, such as
electrons, are to be called matter, and of which, such as positrons, are to be
called anti-matter, but this so-called `T-violation' in physics is irrelevant
for the second law).

Instead, the second law is a statement about the state of the universe
and apparently can be traced back to low-entropy conditions in the very early
universe, but then the question is why the early universe had low entropy. My
guess is that the quantum state of the universe is very special (e.g., as given
by the Hartle-Hawking `no-boundary' proposal, or by the `tunneling proposal' of
Vilenkin, Linde, and others), and that this special state had low entropy near
the beginning. In toy models incorporating the Hartle-Hawking proposal, one
can indeed derive some sort of second law from it, in the sense of getting a
simplified model universe with low entropy at early times but growing entropy
at later times. Thus Moorad is not quite right that there are no theories for
the second law, but it certainly must be admitted that the few theories we do
have for it are highly speculative. The second law is a touchstone, so that
any correct theory for the entire universe had better explain or incorporate

Don Page