Prior to exploring applications to physical problems outside the realm of communication theory, it is useful to pause and examine a second developmental path toward a theory of information. The noted similarity of the Wiener-Shannon information measure to earlier expressions in statistical mechanics is much more than coincidence. Well over a century ago Ludwig Boltzmann's search for a theoretical expression to match Clausius's thermodynamic entropy 
led him to relate entropy to probability. In the form later adopted by Planck in 1906, he suggested in his great paper of 1877 the well-known expression
where k is Boltzmann's constant, and W is roughly the number of a priori equally probable microscopic states of the system compatible with the thermodynamic state. In
classical mechanics it is a phase volume, and in quantum theory it is the measure of a manifold in Hilbert space. Rather then a probability, as Planck's abbreviation for Wahrscheinlichheit implies, W is actually a multiplicity factor, which can be a factor in a probability, of course. Indeed, Boltzmann took as his example the multinomial coefficient and derived the expression analogous to Eq.(2), in which 
is replaced by the frequency of particle occupation of cells in phase space.
The point here is that the theoretical entropy provides a measure of our lack of information about the specific microscopic state of the system (which must be changing continually in any event). It is not certain how far Boltzmann's thoughts proceeded in linking Eq.(5) with information content, but it is quite clear that he knew something to be involved beyond the basic laws of physics. He writes (Ref.15), ``The Second Law can never be proved mathematically by means of the equations of dynamics alone." Rather, conservation of information occurs only in reversible processes, whereas irreversibility reflects a loss of information and a consequent increase in entropy. It seems remarkable that what Boltzmann understood so well over a century ago is still found puzzling by some today.
Unfortunately, these similarities led a number of writers to jump immediately to the conclusion that Shannon's measure (the negative of Wiener's) was in fact identical to the thermodynamic entropy -- a step even Boltzmann declined to take without proof. Chief among the advocates of this leap was Brillouin (Refs.5,16), who coined the term negentropy for Shannon's measure. The desire to make such an identification is understandable; but making it is lamentable, because it was not at all justified at this point on the basis of communication theory alone. The missing link was to be found several years later.