Colin,

`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.`

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CLASSICAL THERMODYNAMICS

`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 = mc^2).`

`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

`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 (PoincarĂ© 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.`

INFORMATION ENTROPY

`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`

http://blog.rudnyi.ru/2010/12/entropy-and-artificial-life.html

`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.`

Evgenii On 15.04.2011 02:27 Colin Hales said the following:

Hi all, I was wondering if anyone out there knows of any papers that connect computational processes to thermodynamics in some organized fashion. The sort of thing I am looking for would have statements saying cooling is ....(info/computational equivalent) pressure is ..(info/computational equivalent) temperature is .... volume is .... entropy is .... I have found a few but I think I am missing the good stuff. here's one ... Reiss, H. 'Thermodynamic-Like Transformations in Information Theory', Journal of Statistical Physics vol. 1, no. 1, 1969. 107-131. cheers colin

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