Stat mech-microstates and macrostates

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In summary, the conversation discusses the basics of statistical mechanics and microstates/macrostates. The speaker has attempted to draw a diagram to explain the concept and is looking for someone familiar with the topic to review it and provide feedback. The two systems in question are compared to a "coin" analogy and the energy exchange between the two subsystems is limited. The speaker also suggests including formulas and explicitly stating the number of microstates, which is related to the binomial and multinomial distributions.
  • #1
Dawei
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Hello,

I'm trying to make sure I understand the basics of statistical mechanics and microstates/macrostates.

Being the nerd that I am, I have attempted to draw a diagram, as if I were explaining it to someone. If some one who is familiar with this topic could please review it and tell me if they see anything at all wrong, I would very much appreciate it.

The two systems are each two state systems, and to keep things simple I used the common "coin" analogy, where the total number of coins represents the total number of particles, and if they are "heads" then that means they are in the upper energy state. The two individual subsystems, as well as the final combined system, are all assumed to be completely closed. The only energy exchange allowed is between the two subsystems after they are in contact.

4301178262_d90074aaf3_o.jpg
 
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  • #2
That's a very good explanation that one rarely finds in a book.

You could even write it out with formulas.

Also you could write out the number of microstates explicitely. In your case it is the binomial distribution. In the more general case it is the multinomial distribution and this is the origin of the well known
[tex]S=-\sum_i p_i\ln p_i[/tex]
 
  • #3


Hi there,

Your diagram and explanation seem to be correct! In statistical mechanics, microstates refer to the specific configurations of particles in a system, while macrostates refer to the overall properties of the system such as temperature, pressure, and energy. In your example, the microstates would be the specific arrangements of heads and tails for each coin, while the macrostate would be the total number of heads or the total energy of the system.

One important concept in statistical mechanics is the idea of entropy, which is a measure of the number of microstates that correspond to a given macrostate. In your example, if all the coins are heads, there is only one microstate and low entropy, but if there is a mix of heads and tails, there are many possible microstates and higher entropy.

Overall, your understanding of stat mech and microstates/macrostates seems to be on the right track. Keep up the good work!
 

FAQ: Stat mech-microstates and macrostates

What is the difference between microstates and macrostates in statistical mechanics?

In statistical mechanics, microstates refer to the specific arrangements or configurations of particles in a system, while macrostates refer to the overall properties of the system such as temperature, pressure, and energy. Macrostates are a result of the combination of microstates and are used to describe the behavior of a system on a larger scale.

How are microstates and macrostates related in statistical mechanics?

Microstates and macrostates are related in statistical mechanics through the concept of equilibrium. In an equilibrium state, the system will tend to occupy the most probable macrostate, which is determined by the number of associated microstates. The more microstates that are associated with a particular macrostate, the more likely it is to be occupied by the system.

Can you provide an example of microstates and macrostates in a real-world system?

An example of microstates and macrostates can be seen in a gas in a container. The individual molecules of the gas represent the microstates, while the overall properties of the gas such as temperature, pressure, and volume represent the macrostate. Each microstate of the gas contributes to the overall macrostate, and the behavior of the gas can be described by studying the distribution of these microstates.

How does the number of microstates affect the entropy of a system?

The number of microstates in a system is directly related to the entropy of the system. As the number of microstates increases, the entropy of the system also increases. This is because a higher number of microstates means a higher number of possible arrangements or configurations of particles, which leads to a greater disorder or randomness in the system.

Can macrostates be used to predict the behavior of a system?

Macrostates provide a useful way to describe the overall properties of a system, but they cannot be used to predict the behavior of individual particles within the system. This is because macrostates are a result of the combination of microstates and do not provide information about the specific arrangements or interactions of particles. To fully understand the behavior of a system, both microstates and macrostates must be considered.

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