Volume constraint in micro-canonical derivation of statistical physics

In summary, the use of the micro-canonical ensemble in deriving distributions involves the requirement of a constant total volume for the system. This constraint is not explicitly stated, but it could be inferred as a way to ensure that the system is closed. The energy levels of the system may change continuously with a slowly varying volume, but the assumption of fixed energy levels implies a constant volume.
  • #1
Philip Koeck
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Another question about the use of the micro-canonical ensemble in deriving distributions.

On the Wikipedia-page the authors mention that the total volume of the system has to be constant.
See: https://en.wikipedia.org/wiki/Bose–Einstein_statistics#Derivation_from_the_microcanonical_ensemble

On the other hand this statement is not used as a constraint or in any other way that I can see.

In a way it would however make sense to introduce a volume constraint in order to make sure the system is closed.
If V is not constant (meaning W is not zero), but U is constant, then Q is not zero and the system is not closed (at least for an ideal gas).

Does anybody know about volume constraints in the microcanonical picture?
 
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  • #2
In E = ∑niεi one has generally E = ∑niεi(N,V). Each εi changes in a continuous manner if V is vhanged infinetely slowly.
 
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  • #3
Lord Jestocost said:
In E = ∑niεi one has generally E = ∑niεi(N,V). Each εi changes in a continuous manner if V is vhanged infinetely slowly.
So the volume constraint is not used explicitly, but if the energy levels ei depend on the volume then the assumption of fixed energy levels implies a constant volume.
Is that correct?
 
  • #4
One can see it in this way.
 

FAQ: Volume constraint in micro-canonical derivation of statistical physics

What is the volume constraint in micro-canonical derivation of statistical physics?

The volume constraint in micro-canonical derivation of statistical physics refers to the assumption that the total volume of a system remains constant during the course of a physical process.

Why is the volume constraint important in statistical physics?

The volume constraint is important because it allows for the derivation of fundamental thermodynamic quantities, such as energy and entropy, in a closed system. It also helps to define the boundaries of a system and understand how it interacts with its surroundings.

How is the volume constraint applied in statistical physics?

In statistical physics, the volume constraint is applied by considering the total number of microstates that are accessible to a system within a given volume. This allows for the calculation of the probability of a particular macrostate and the derivation of thermodynamic quantities.

What are the implications of violating the volume constraint in statistical physics?

If the volume constraint is violated, the system is no longer considered to be in a micro-canonical ensemble and the assumptions made in the derivation of statistical physics equations may no longer hold. This can lead to inaccurate predictions and results.

Are there any exceptions to the volume constraint in statistical physics?

There are certain cases where the volume constraint may not apply, such as in systems with a changing volume due to external work or in systems with a variable number of particles. In these cases, different ensembles and methods must be used to accurately describe the system.

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