There was a thermodynamics related question on the everything-list
and my answer is below.
I used to work in chemical thermodynamics for awhile and I give you the answer from such a viewpoint. As this is the area that I know, then my message will be a bit long and I guess it differs from the viewpoint of people in information theory.
First entropy has been defined in classical thermodynamics and the best is to start with it. Basically here
The Zeroth Law defines the temperature. “If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other”.
The Second Law defines the entropy. “There exist an additive state function such that dS >= dQ/T” (The heat Q is not a state function)
The Third Law additionally defines that at zero K the change in entropy is zero for all processes that allows us to define unambiguously the absolute entropy. Note that for the energy we always have the difference only (with an exception of E = mc2).
That’s it. The rest follows from above, well clearly you need also the First Law to define the internal energy. I mean this is enough to determine entropy in practical applications. Please just tell me entropy of what do you want to evaluate and I will describe you how it could be done.
A nice book about classical thermodynamics is The Tragicomedy of Classical Thermodynamics by Truesdell but please do not take it too seriously. Everything that he writes is correct but somehow classical thermodynamics survived until now, though I am afraid it is a bit exotic. Well, if someone needs numerical values of the entropy, then people do it the usual way of classical thermodynamics.
Statistical thermodynamics was developed after the classical thermodynamics and I guess many believe that it has completely replaced the classical thermodynamics. The Boltzmann equation for the entropy looks so attractive that most people are acquainted with it only and I am afraid that they do not quite know the business with heat engines that actually were the original point for the entropy.
Here let me repeat that I have written recently to this list about heat vs. molecular motion, as this give you an idea about the difference between statistical and classical thermodynamics (replace heat by classical thermodynamics and molecular motion by statistical).
At the beginning, the molecules and atoms were considered as hard spheres. At this state, there was the problem as follows. We bring a glass of hot water in the room and leave it there. Eventually the temperature of the water will be equal to the ambient temperature. According to the heat theory, the temperature in the glass will be hot again spontaneously and it is in complete agreement with our experience. With molecular motion, if we consider them as hard spheres there is a nonzero chance that the water in the glass will be hot again. Moreover, there is a theorem (Poincaré recurrence) that states that if we wait long enough then the temperature of the glass must be hot again. No doubt, the chances are very small and time to wait is very long, in a way this is negligible. Yet some people are happy with such statistical explanation, some not. Hence, it is a bit too simple to say that molecular motion has eliminated heat at this level.
Shannon has defined the information entropy similar way to the Boltzmann equation for the entropy. Since them many believe that Shannon’s entropy is the same as the thermodynamic entropy. In my view this is wrong as this is why
I believe that here everything depends on definitions and if we start with the entropy as defined by classical thermodynamics then it has nothing to do with information.
INFORMATION AND THERMODYNAMIC ENTROPY
Said above, in my viewpoint there is meaningful research where people try to estimate the thermodynamic limit for the number of operations. The idea here to use kT as a reference. I remember that there was a nice description on that with references in
Nanoelectronics and Information Technology, ed Rainer Waser
I believe that somewhere in introduction but now I am not sure now. By the way the book is very good but I am not sure if it as such is what you are looking for.