There are those for whom the complicated behavior seen in
otherwise-simple dynamical systems is reminiscent of
many-body systems and the necessary
statistical descriptions associated with them. Indeed, some have
been led by this to an inverse implication -- namely, that
chaotic particle motion underlies the need for a statistical
description in the first place. That is, we are to believe that it
is the Liapunov exponents for individual-particle orbits
which provide the mechanism for mixing, and
for the filamentation envisioned by Gibbs (and achieved through
coarse-graining). Moreover, it is even argued that
exponentially-divergent particle trajectories in a gaseous system
are the `ultimate' source of irreversibility, in the sense that
such pair-orbit separation represents a stirring of phase space.
(A particularly lunatic advocacy of this sort is offered by
McCauley. 
)
To appreciate fully the origin of these feelings it is necessary to
review in moderate detail a number of related views on
many-body systems that have accumulated and hardened over the years
in some quarters, for only then is one able to grasp the motivation
behind these desires to link chaos with thermodynamic
systems.
Let us begin with the words of a contemporary worker in this area,
referring to what he believes is one of the long-standing
questions of statistical mechanics 
:
Where does the randomness necessary for statistical behavior come from if the universe is at heart an orderly, deterministic place?"
Our first thought is to wonder about the role of randomness at all. In a gas, for example, just what is it that is random? We must certainly have faith that the constituent particles obey the known equations of motion, classical or quantum, and simple linear Hamiltonians have led to macroscopic predictions in close agreement with experiment for over a century. The behavior we observe is just physical behavior, following deterministic physical laws, and it is difficult to understand what could possibly be meant by `statistical behavior'. Surely the particles are not aware of our need to describe them so! We shall return to the question of randomness below, along with some comments about persistent attempts to impress human will upon Nature.
Further thoughts from the same source are similarly
puzzling 
:
[the] success of statistical mechanics for many-body problems is prima facie evidence supporting the existence of a transition from orderly to highly erratic orbital motion in Hamiltonian systems as particle number is increased."
That is, independently of how the particles interact, the
mere act of adding a few more to the system induces extraordinary
qualitative changes in the particle dynamics -- and this,
presumably, for any density and temperature. It would seem to
stretch credulity beyond the elastic limit to believe that N can
play such a role in the system. Certainly there is no direct
evidence of any kind for equations of motion evolving like this.
If one tends to think this way, however, it is then not very much
of a step to assert next 
that
thermodynamics assumes
all many-body systems to be chaotic, implying that most system
motions are so complex they are not controllable by any macroscopic
means." That we have only macroscopic control
over such systems is precisely the point, of course, but lack of
this control over microscopic particle motions by no means implies
that these motions are particularly complex or `chaotic' on a
microscopic scale. Rather, there are simply no Maxwell demons.
To say that heat is energy of uncontrollable chaotic system
motions" is only to re-emphasize that lack of control, with or
without inclusion of the word `chaotic'. To go further and suggest
that interpretation in terms of nonlinear microscopic dynamics
can lead to practical violations of the second law of
thermodynamics, as is done here, serves only to increase our
incredulity.
The idea that merely increasing N brings about a transition to
chaotic behavior has also been employed in a more direct physical
manner. Ford 
describes a purely mechanical
model in which increasing N purportedly induces a metamorphosis
from sound to heat, dutifully identified with the transition
. The claim is made that chaos is the
sole essential feature needed to obtain a diffusive energy
transport." It is difficult to know what to make of this notion
if, with the present author, it is believed that the essential
feature of sound is the correlated propagation of density
fluctuations over large distances -- in a typical lecture hall
some 
mean free paths. The intensity decays, to be sure,
owing to absorption mechanisms having nothing to do with `chaos',
and some of that energy may eventually appear as an increase in
kinetic energy of the particles. It is a subtle weldbilt
indeed that can mimic this physical behavior merely by
increasing particle number.
As an aside, we note that the physical difference between sound and
heat, for example, has been well understood for many years.
Although a fluid containing 
particles possesses
correspondingly many degrees of freedom, upon perturbation from
equilibrium most of these relax very quickly to their equilibrium
values. The observation of only a few long-lived macroscopic modes
corresponds to the existence of only a few locally-conserved
quantities, which are related to the microscopic conservation laws.
Because they satisfy local conservation laws, local excesses of
these quantities disappear neither locally nor quickly, but relax
by spreading out over the entire system. In a simple fluid these
hydrodynamic modes consist of three propagating sound modes,
two non-propagating shear waves, and a thermal diffusion
mode. 
The ability to reduce everything to simple fundamental laws
does not imply the ability to start from those laws and reconstruct
the universe". 
And thus we come to the notion of
organizing principles, the understanding of which concerns
all of science, and particularly statistical physics. These range
from crystallization and DNA to self-organization and synergetics,
and have always presented us with exquisite challenges. For
example, no one has ever succeeded in deriving the crystal lattice
directly from the Schrödinger equation. Beyond these, the
importance of such principles can be seen in the health of the
Gestalt movement in psychology after almost ninety years.
Because we see structure in turbulence and root systems,
say, it is legitimate to seek possible `order in chaos' hinted at
by advances in nonlinear dynamics. Perhaps the greatest legacy of
these current insights will indeed be to illuminate many of the
organizing principles of Nature.
But at the same time we wonder how the detailed microscopic behavior, nonlinear or not, can bear on the issue of statistical descriptions of that behavior. It is primarily because those details are almost irrelevant that statistical mechanics gives the incredible agreement with experiment that it does. And free-particle models often work very well, where there are no nonlinearities at all in the basic Hamiltonian -- e.g., the free-electron theory of metals. (Actually, there is an organizing principle at work here in the form of screening, but that is intrinsic to the Coulomb potential rather than chaotic orbits.) We are not concerned with sensitivity to initial conditions at the microscopic level because the need for a statistical description arises fundamentally from our inability to control them in any event, and we are totally unable to predict microscopic motions in many-body systems. (The beauty of ion-trap experiments, of course, is that now one can study some properties of a single particle in detail.) But we do have faith that the microscopic motions follow the laws of physics, and that turns out to be almost all we need to know. It is very difficult to see how any single prediction of statistical mechanics would be qualitatively changed were the microscopic Hamiltonian nonlinear and conditions established such that the orbits were `chaotic'. At most one would expect only a change in the density-of-states of some system, say, which could lead to some new physics, but the basic principles behind the statistical method of analysis would not have changed one bit. Such new physics, of course, has yet to be seen. Moreover, the equations of thermodynamics follow from the partition function,
so that any additional `wiggles' in the density-of-states are integrated out anyway.
To belabor the obvious in another aside, we re-emphasize that there would be no point to studying physics if there were no deterministic physical laws. What the recent issues in nonlinear dynamics tell us is that it is necessary in describing certain processes to ask new and different questions about them, and to define anew the class of experimentally reproducible processes -- the latter are already well known for much of classical thermodynamics.