Calculating Entropy of 2D Free Particles: Statistical Physics Challenge

In summary, the conversation is about finding the entropy of N>>1 free particles moving in a 2d box with energy E using the quantum canonical ensemble. There is confusion about whether to use the quantum canonical or microcanonical ensemble and how to compute the partition function and eigenvalues of the density operator. There is also discussion about the lack of information about the volume of the box and temperature in the problem.
  • #1
Palindrom
263
0
Hi all.

So something's bothering me;

Given the def. S=-k(sum on r: pr*ln(pr)) for the entropy, find the entropy of N>>1 free particles moving in a 2d box with energy E.

Now, don't I have a continuum of states here? How do I do that?

Thanks :smile:
 
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  • #2
Use the quantum canonical ensemble...Compute the partition function and then the entropy.

Doesn't mention anything about the temp...Could it be the microcanonical ensemble...?:confused:

Daniel.
 
  • #3
Hum... you've kinda just given me a dizzy head... :smile:

It's only my second week of statistical mechanics, so consider that.

And... I might not recognize some of the terms in English. What's a partition function?

Sorry :rolleyes:
 
  • #4
The problem is weird,as it doesn't mention about the volume of the box,nor the temperature.That would mean the microcanonical ensemble,but again i can't see a way to compute the eigenvalues of the density operator.

Daniel.
 
  • #5
What density? Of states?
Weird anyway... I'll keep thinking about it.
 

1. What is entropy in statistical physics?

Entropy is a measure of the disorder or randomness in a system. In statistical physics, it is used to describe the number of possible microstates that a system can have, given its macrostate.

2. How is entropy calculated for 2D free particles?

The entropy of 2D free particles can be calculated using the formula S = k ln(W), where S is the entropy, k is the Boltzmann constant, and W is the number of microstates available to the particles.

3. What is the significance of calculating entropy in statistical physics?

Calculating entropy allows us to understand the behavior and properties of a system on a microscopic level. It also helps us to predict the likelihood of a particular state or configuration occurring.

4. Can entropy be negative?

No, entropy cannot be negative. According to the second law of thermodynamics, the entropy of a closed system will always increase or stay constant, but it can never decrease.

5. Are there any real-world applications of calculating entropy for 2D free particles?

Yes, calculating entropy for 2D free particles has applications in various fields such as materials science, chemistry, and biology. It can be used to understand the behavior of gases, liquids, and solids, as well as the thermodynamics of chemical reactions and biological systems.

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