Question

I am trying to learn statistical mechanics on my own, but I am having trouble understanding what exactly is a microstate. I kind of have a vague idea by imaging it as kind of configuration of each particle.

Answer 1

A microstate is a description of a system, by the use of the constituting atomic configuration.
It is very important actually to associate the words macrostate and microstate to the words "energy level" and "energy state".. So lets:
For a micro state we talk about energy states. Each configuration you can think about is associated with some energy which constitutes a energy state. All microstates with the same energy, can be considered a "energy level". The microlevel is associated with a macrostate as we can not tell the microstates a part from a macroscopic treatment.

I've made an example in the attachment below.

Answer 2

We might as well define another word: The amount of microstates in a macrostate we call the degeneracy and is important within the Boltzmann distribution.

Answer 3

Ok, so how do we tell different microstates apart, what if they have the same energy, how do we distinguish them from each other? I kind of think in a classical mechanics way and say that by , at least in principle, specifiing each particile's position and momentum is a way to specify microstates.

Answer 4

You can't tell them apart from a macroscopic level. That is indeed the idea of thermodynamics, we can only measure the macroscopic property as the cause of all these microstates. You can imagine the idea in your head, to keep track of all particle positions and momenta in 1 L of gas.

You are indeed right. If you want to know each microstate you need to know all their positions and momenta. It however turns out there that a system can exist in a discrete, but possibly infinite set of microstates. The number of microstates can be shown to be proportional to the phase space the system occupy. In general the number of microstates is depending on all the thermodynamic variables you know from the state functions.

For simple modeling work (assuming now you don't want to calculate the amount of microstates) we can approximate and just write up the different microstates as a function of their degrees of freedom. This is what I did in the example I showed earlier, and the energy is significantly different when a bond occur in the polymer.

All the microstates do not need the same energy to be treated by statistical mechanics. It is very common that we define an ensemble of molecular conformations to be treated as 1 micro/macro- state, instead of just one.

Answer 5

If you want to challenge your self try derive an expression for the number of microstates as a function of energy for N particles in a three dimensional space. You can skip the normalization due to (in)distinguishability and just write what the number would be proportional to.

Answer 6

If you plan on doing more statistical mechanics and also try do some experiments your self I can highly recomend trying the molecular workbench:

http://mw.concord.org/modeler/

It is an amazing yet simple tool to do computational experiments with statistical mechanics and to explain the classical thermodynamics most chemists use.