Thermodynamics: A Dynamical Systems Approach – Introduction

The text is written in December 2008. I review the first chapter, Introduction of the book Thermodynamics: A Dynamical Systems Approach by Wassim M. Haddad, Vijay Sekhar Chellaboina, & Sergey G. Nersesov

The first chapter is available for free from Princeton University Press

In Introduction there is an enjoyable overview of thermodynamics, a short overview of system thermodynamics and then an outline of the book. I should say that during the first reading the section about system thermodynamics was hardly understandable. Now I am reading the book for the second time and I already can follow it. Yet, it does not make sense to make comments about it right now; I’d better do it while commenting on other chapters. Hence I limited my comments in this message to Section 1.1 An overview of thermodynamics.

I like this section. It is a concise summary and nice text. Actually I have decided to buy the book only after I have read it for free from Princeton Press. It was a very clever advertisement for the book.

1) Thermodynamics and Universe

I guess since Clausius (“The entropy of the Universe tends to a maximum”) there are some fascinating relationships between thermodynamics and the Universe. There is hardly a textbook where this has not been discussed. The authors have stuck to this tradition and mentioned this several times.

I am personally sceptic if the thermodynamics laws could be applied to the Universe. First, thermodynamics assumes that energy and entropy are additive functions. It seems not to be valid in the case of Universe. Second, I find it dangerous to extrapolate models too far away.

Recently I have found a fascinating site Are You Living In a Computer Simulation?

I think that this is a good example that shows the danger of extrapolation. But if we speak about thermodynamics itself, then it actually does not matter if we live in a simulation or not. A good reading in this respect is The Matrix as Metaphysics

The concept of expanding universe could suffer, but the thermodynamics remains the same.

2) Thermodynamics is hard to teach

The authors make several good statements about this. I would agree. It would be nice to have more logic here. Recently I have read The Tragicomical History of Thermodynamics by Truesdell and this aspect of thermodynamics is nicely covered there.

The best characteristics of thermodynamics that I have seen is

“Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you any more.”

This is attributed to Anold Sommerfeld on

I would say that this is the very true. When one starts using the thermodynamics in practice, then actually it is okay. I have seen no problem by using the thermodynamics laws in chemical thermodynamics. So it was my strategy in teaching, to bring students to the third level as soon as possible.

3) Equilibrium and nonequilibrium states

In order to shows inconsistency in conventional thermodynamics, the authors give a simple example on p. 8 with the conclusion “Hence, the entropy of the system can only increase if the system is not isolated!” The solution in chemical thermodynamics to this apparent paradox is quite simple – introducing so called a frozen state. Imagine a box with gases that could react with each other but the reaction rate is negligible. Then we have some equilibrium state that could be changed by exposing gases to a catalyst. This is a pretty standard example in chemical thermodynamics. I guess that it would make sense for mathematicians to start learning thermodynamics from chemical thermodynamics and only after that go to heat engines. Unfortunately along this way they first have to learn a bit of chemistry and this makes such a suggestion completely unfeasible.

4) Modern thermodynamics

At the end of this section the authors list modern works on the foundation of thermodynamics. To my shame I have completely missed them. Just recently I came across Rational Thermodynamics by Truessdel but have not read it yet. It is a tough reading for a practitioner.

There is a nice paragraph about rational thermodynamics in the section (p. 10) but unfortunately the authors have decided not to disclose what is wrong with it. And if they decided to write their own book, then presumably there should be something in rational thermodynamics with what they do not quite agree. However, the authors have concealed that reason. It is a pity. I have to read Rational Thermodynamics by myself.




Chapter 2: Dynamical system theory
Chapter 3: A System Foundation for Thermodynamics
Chapter 4: Temperature Equipartition and the Kinetic Theory of Gases
Chapter 5: Work, Heat, and the Carno Cycle
Chapter 6 and 7