New Countries and Physics

What do Scotland's independence and Einstein have in common?

Well statistical physics of course!

What is statistical physics, you ask? Statistical physics is the study of large systems consisting of many elements.

Well then isn't every science statistical physics? Everything can be considered as a system consisting of lots of parts... right? An animal is made of many cells, a society is made up of numerous people, an economy is made of countless people and countless dollars, a block of wood is made of many atoms. Are these all statistical physics?

Of course not! In stat. phys. you examine large systems consisting of many elements in a way that you try to only focus on the fact that they are built up from many many many small pieces. You start examining a system based on the behavior of these building blocks, using as few properties of them as possible. Which is why it is so cool, actually! Everything I talked about in the last paragraph: biology, sociology, economics, other areas of physics all make use of statistical physics - the application of stat. phys. on already otherwise examined systems gives new insights on the fundamental working of them.

Now traditionally, statistical physics was used to describe the attributes of gases - their pressure, volume, temperature, and things like this. Basically it was the part of physics that wanted to explain why (the thoroughly experimented and well-known) thermodynamics worked the way it did, by starting out from the behavior of the building blocks: gas molecules. But very soon people started to realize that the methodology and the explicit results of statistical physics could be applied to other, totally different systems - for example economics.

So here I'd like to give you a view on how a physicist (me) views the Scottish independence intention. First I'll give you a simple visualization of the difference between a tight and a loose system, using the Boltzmann argument, which is interesting in itself, I think.

\begin{physics}
If the temperature ("T"), the volume and the particle number of a system is fixed, then to reach an equilibrium state (in other words the preferred state), the "F" free energy must be minimized, where F = E - TS (where the following are the relevant system parameters: F=free energy, E=energy, T=temperature, S=entropy). This is similar to what you learn in high school, when you're told that the principle of energy minimization holds; except now the free energy must be minimal.

Now consider this: if T is small (it's very cold), then even at large S (large disorder of the system), the -TS component is secondary compared to the E, in other words F is about equal to E => minimizing F is the same as minimizing E. For example in some arbitrary units E is 1000, S is 50000, and T is 0.00001, then E - TS = 1000 - 5 = 995 which is about E.

On the contrary, if T is large (it's really hot), then the effect of the entropy, S, of the system will be amplified (simply because it's multiplied by a large number), so it counts a lot, and the E energy of the system will give only a minor contribution to F. For example if E=1000, S=50000, T=1, then F= -49000, which is almost the same as if we wouldn't even calculate with the energy, in other words -50000.

This way, at small temperatures the energy (E) must be minimized, and at large temperatures entropy (S) must be maximized! You minimize the energy of a system by putting its atoms at an ideal distance from each other, which results in tight and rigid crystalline structure (this is a state with small entropy, which systems usually don't like, but in this case the entropy doesn't matter, remember?). Or, if it's really hot, then you can maximize the entropy by maximizing the disorder of the system, meaning that the system components fly around in every direction completely individually.
\end{physics}

On the top you have a gas, a high entropy and high energy system. On the bottom you have a solid, which is a low entropy and low energy system. Both systems minimize the F=E-TS function, the only difference is that at different temperatures it is minimized in different ways...  which leads to the different phases of matter.

The previously described model is used for understanding the basics of why there are different phases of matter (gas, liquid, solid).

It is also a terrible model (in itself) for describing the changes in country sizes throughout history, and for describing the need for independence in people. However, it is a pretty good starting point for a model that gives insight on this! As you can see, this model describes how a system radically changes its structure and behavior due to a circumstance, in this case the temperature. The only assumption for this model is that there is an optimum particle-to-particle distance, in which the energy is minimized, and this distance is very small.

So starting from this, or from other models or intuitions from statistical physics, it is possible to generate models for how trends in country sizes change in time. Most of these models would use the amount of resources of a country (usually associated with the energy of the system) as an external parameter. These resources can be natural, financial, intellectual, spiritual resources, or even security resources! (For example a country would have large security resources if it would be safe from every kind of military threat.)

By changing the resources of a system, its structure usually changes. For example less resources would lead to tighter bonds between parts of the system, (e.g. World War ally systems; Russia's threat today and the NATO's response; groups of people facing common problems, (this could be students having a tough time at school, or boy scouts getting soaked in the rain while pitching their tent, or people at alcoholic meetings discussing their problems)). On the other hand, more resources usually lead to the parts of the system separating, lead to fragmentation and looser bonds (think of high entropy!)

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Network theory, which has much to do with statistical physics, is another part of science, which lets us assume similar things: networks with more resources tend to have looser connections, but with more random connections between previously unconnected nodes. On the contrary, networks with fewer resources generally have nodes forming tight connections with a less amount of nodes (note: the points of a network are called nodes). And by the way this is also true for your personal life! In times when everything is fine, you are open to lots of new people and enjoy getting to know random people, whereas when times are more difficult, or you have a bad day, you resort to your good friends, and family becomes more important.

A good example from a non-social network is also your neural network, in which the brain's "open-ness" to new things is totally different in different circumstances. Financial investment networks also exhibit similar phenomena. And some connection can also be made with a previous post about Boundaries, where I wrote about 'more boundaries = more efficient system', and 'less boundaries=more creative system'.

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My point was to show you how statistical physics and network theory can be used to gain more insight on many parts of life, such as the independence of nations. I showed you a simple physical model in connection with phase transitions, the Boltzmann model. I also tried to convince you that there are more sophisticated models, which can be built to describe social, political, financial, biological systems, and that all of these topics can also be viewed from a slightly different angle using network theory.

I think it's always fun to step back and see how large systems and networks exhibit very similar behavior - try it out in your own life even on smaller networks, systems! Hope you enjoyed the post :)