I have just started re-reading Thermal Physics, by Kittel and Kroemer. They state the fundamental assumption of thermal physics as:

...a closed system is equally likely to be in any of the quantum states accessible to it. All accessible quantum states are assumed to be equally probable - there is no reason to prefer some accessible states over other accessible states.

I previously thought I understood the fundamental assumption, but apparently I do not. For an isolated system (where the number of particles and total internal energy are constant), this makes sense, but how can it be true for a closed system?

I think the issue is that the author is defining what is meant by a "closed system" differently to every other textbook I've read. Indeed, he goes on to write:

A closed system will have constant energy, a constant number of particles....

I always thought that such a system was thermally isolated, and that a closed system could have variable energy but has constant particles.

Is Kittel defining the concept of a closed system to be different to other authors, or am I simply misunderstanding something vital?

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    $\begingroup$ I am pretty sure closed usually means constant $N$, while isolated is constant $N$ and $E$. As you stated, the authors probably just chose a different vocabulary convention. If a system is non-energetically isolated states are no longer equally probable. $\endgroup$
    – Dimitri
    Feb 17, 2016 at 13:34
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    $\begingroup$ I think the answer is in your question. Kittel defines what he means by closed and makes his statement accordingly. Different people have different vocabulary. Often, there is no accepted standard. $\endgroup$
    – garyp
    Feb 17, 2016 at 13:50
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    $\begingroup$ Thanks to you both for your comments. I was quite sure that this was the case, but I was worried that the problem was more subtle. $\endgroup$
    – Lachy
    Feb 17, 2016 at 13:52

1 Answer 1


Well, Arnold Sommerfeld once said;

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, so it doesn't bother you any more.

But I do not think that is the issue here.

You are right in that Kittel is not using the generally accepted modern terminology but luckily he explains what he means by a closed system. Three different systems in thermodynamics are; open systems in which the system can exchange matter an energy with environment, closed systems in which energy can be exchanged with environment but not matter and isolated systems in which neither energy nor matter can be exchanged.

  • $\begingroup$ Ok, thanks for the clarification. Indeed: those are the definitions of open, closed and isolated that I am familiar with, I just thought my confusion might be due to something more subtle. $\endgroup$
    – Lachy
    Feb 17, 2016 at 13:55

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