The zeroth law of thermodynamics states that if two thermodynamic
systems are each in thermal equilibrium with a third, then they are in
thermal equilibrium with each other. Accordingly, thermal equilibrium
between systems is a transitive relation.
Combinatorics is quite frankly an ocean with a wide variety of applications. But since you ask, let’s take a look at the example of a ‘Two state Paramagnet’.
What is a paramagnet?
A paramagnet is a material in which the particles like compass needles align parallel to any applied magnetic field. But it is a temporary effect and the magnetization is lost when the field is removed
Paramagnetism in Liquid Oxygen
One of the popular examples of paramagnetism is liquid oxygen.
When oxygen is liquefied and poured over a magnet, the magnetic effect of the electrons become substantially noticeable.
Molecules will align to the magnetic from the
magnet creating an induced magnetic field of its own.
As the liquid oxygen boils off you can you can see for a moment a ‘mist’ that it gives off that is still attracted to the magnets. – Paramagnetism
But how many particles are aligned with the field?
So, what can you do with that ?
One can find the net magnetization produced by the material based on the total number of dipoles facing up or down.
And essentially the total energy of the system (neglecting any interactions between dipoles).
We have come a long way from a simple combinatorics formula, now haven’t we?