# Entropy

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The notes are attached.  See related notes on thermodynamics.

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### Re. definitions of fundamental thermodynamic terms

I am not sure if I can be happy with the definition of a system as "a part of the world." Thermodynamic statements can be made about the entire world taken as a system too.

Therefore, I think the focus of the definition should be put on the *objects* under study---by which the way they are put together also is included. (The principles or rules governing the way the objects are put together, do have thermodynamic entailments.) Sometimes, the set of objects under study may in principle include all objects in the world. The definition would remain unstrained even for application to this case.

The whole thing might seem hair-splitting at this stage, but consider the next defintion.

"An isolated system is one that does not interact with the rest of the world." Fine. What about the entire world taken as a system? Is this system open? closed? isolated? It is usually said to be isolated. But why? If we try to apply the given definition, doesn't it involve making a reference to nothing?

Instead, how about this definition (just a small change): "An isolated system is one which does not interact with any other object/system."

Here, the tricky issue of whether we know if there is any object left outside of the system under consideration or not, is made silent, i.e. a non-issue. I hope it does.

The whole idea is that with with open systems, you have to put theoretical sentries at the borders---you have to worry about all sorts of things that get exchanged at those borders---matter, energy (heat), work. In contrast, with closed systems, you know that mass (practically, the same as matter) won't get exchanged at the borders but energy and work might. In contrast to *both* these, with isolated systems, you simply don't bother putting a sentry in the first place---the system formulation has been so abstracted away from the concrete reality that you don't have to bother about that part.

To conclude, ask the question: What is it that an isolated system is isolated from? The usual answer is: From everything else (aka the enviornment).

But following my speculation, I think another, epistemologically deeper, perspective is possible. The answer can be: from certain theoretically complicating aspects of the concrete reality, via a process of abstraction that removes interactions out of the theory via appropriate limiting processes. Thus, the isolation in question is rather about abstracting away than about "air-tighting", "energy-tighting", "work-tighting", in short, "everything-tighting" away. Once you understand this part, a lot of questions arising in physical application---whether in cosmology or concerning accurate experimental realization---begin to better fall in place.

Just some food for thought. I think I am onto something right, but won't argue about it. (And, yes, it's easily possible that others have said exactly the same points---including the epistemological points---before me.)

--Ajit

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[E&OE]

### updated notes on entropy

I have just updated my notes on entropy.  I hope to use the notes in teaching the undergraduate course on engineering thermodynamics this fall.

### Re: updated notes on entropy

I added a very short section on the quantum mechanics of hydrogen atom.  This way I can talk about quantum states of isolated system using a concrete example.

### Slides on entropy

I have just added slides on entropy based on my written notes.

### Toy model to explain physics of entropy

To help young students understand entropy, there is a very useful little "toy model" that my husband Jonathan Selinger just published in his new book, "Introduction to the Theory of Soft Matter." It is in the first chapter. It's a Springer e-book available online here:

It's available free to anyone at a university that licenses the Springer e-book collection. (Users in Ohio can also access it through Ohiolink.)

It's the best way I know to help students understand the fundamental concepts of energy, entropy, free energy, and temperature.

A simple Monte Carlo simulation of the toy model can also help illuminate these concepts.

In my intro-level graduate class on computational materials science I also teach about detailed balance using a different toy model. Each student in the class is told they can have two possible states in this model: standing (high energy) and sitting (low energy), with transition attempts at discrete time steps. We assign a transition rate at each time step of 1 for high-> low and a transition rate of 0.5 for low-> high, determined with an independent coin flip for each student. The question is, in steady state, what is the average fraction of the students that are in the high energy/standing state?

-Robin Selinger

### Notes on entropy are updated

In this version, I moved a few more items to suplemeents.  I have also modified a few places.