# Statistical mechanics and macrostates

• Nylex
In summary, the conversation discusses the number of macrostates in a system of atoms in a box with an imaginary partition and the relationship to the number of atoms. It is noted that for n atoms, there are n + 1 macrostates. The conversation also mentions the different statistics that may apply for identical or non-identical particles, and how a macrostate can be described using a n-tuplet. Finally, the conversation touches on the concept of macrostates for photons and how it depends on the type of particle in the system.
Nylex
In my Statistical Physics and Entropy module, we did something about atoms in a box with an imaginary partition down the middle, so atoms could either be on the left or the right. If there were 4 atoms in the box, the system would have 5 macrostates. If there were 8, there would be 9.

Is is true that for n atoms in such a box, there are n + 1 macrostates, for any n?

Thanks.

Wrt what statistics...?If those atoms are identical,then u'd have 3 possible cases:Maxwell-Boltzmann statistics,Fermi-Dirac and Bose-Einstein.

If they're not identical,then it wouldn't matter what classical/quantum description u adopt...

Either way,a macrostate would be described through a n-tuplet (1,2,...,n) for distinguishable particles or (1,1,...,1) for indistinguishable particles.

Daniel.

If your macrostate is defined as the number of atoms in the left side of the box, then yes, since you can have 0,1,2,..., or n atoms on the left.

dextercioby said:
Wrt what statistics...?If those atoms are identical,then u'd have 3 possible cases:Maxwell-Boltzmann statistics,Fermi-Dirac and Bose-Einstein.

If they're not identical,then it wouldn't matter what classical/quantum description u adopt...

Either way,a macrostate would be described through a n-tuplet (1,2,...,n) for distinguishable particles or (1,1,...,1) for indistinguishable particles.

Daniel.

As usual, I have no idea what you mean.

Galileo said:
If your macrostate is defined as the number of atoms in the left side of the box, then yes, since you can have 0,1,2,..., or n atoms on the left.

Thanks.

If those 4 particles are photons,how many macrostates do you have there...?

Daniel.

dextercioby said:
If those 4 particles are photons,how many macrostates do you have there...?

Daniel.

It was the easiest example to what i'd been trying to tell...It matters what kind of particles you have there...It's not the same thing if they're billiard balls,fermions or bosons...

Daniel.

## 1. What is statistical mechanics?

Statistical mechanics is a branch of physics that uses statistical methods to explain the behavior of a large number of particles, such as molecules, atoms, or subatomic particles. It aims to understand the macroscopic properties of a system by studying the microscopic behavior of its constituent particles.

## 2. What are macrostates in statistical mechanics?

Macrostates refer to the collective properties of a system that can be described by a set of macroscopic variables, such as pressure, temperature, or volume. These variables represent the average behavior of a large number of particles in a system.

## 3. How is statistical mechanics related to thermodynamics?

Statistical mechanics is closely related to thermodynamics, as it provides a microscopic understanding of the macroscopic laws of thermodynamics. It explains how the behavior of individual particles leads to the observed macroscopic properties of a system.

## 4. What is the difference between microstates and macrostates?

Microstates refer to the specific configuration of a system's constituent particles, while macrostates describe the collective behavior of these particles. In other words, microstates are the individual "snapshots" of a system, while macrostates represent the overall "picture" of the system.

## 5. What are some applications of statistical mechanics?

Statistical mechanics has numerous applications in various fields, such as chemistry, biology, and materials science. It is used to study the behavior of gases, liquids, and solids, as well as complex systems such as proteins and polymers. It also plays a crucial role in understanding phase transitions and the behavior of systems at different temperatures and pressures.

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