Counting the number of configurations (Entropy)

In summary, Roger Balian discusses how entropy can be calculated by counting the number of locations in a given phase space that are available for a particular number of particles. He also mentions that this calculation can be done for gas particles in a closed container, if the speeds of the particles are kept small.
  • #1
naima
Gold Member
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Hi all,

Entropy uses the 6N dimensional phase space. But ...
Roger Balian in "Scientific American" takes one liter gas in a cube and he writes:
I can replace the continuous volume by Q = 10^100 sites after having
evacuated the speeds (he says this is possible with quantum mechanics)
He then counts the number of possible places for the N molecules and get the entropy.

How can he do that?
 
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  • #2
I guess he is considering very fast processes in which the modifications on the wall of this cube does not introduce modifications in the pattern of velocities, just the number of positions available will change, so, in order to evaluate the entropy variation one has only to monitor the number of available positions.

I am not sure.

Best wishes

DaTario
 
  • #3
Surprisingly, the distance between 2 sites is like Planck's length!.
Is it really correct to ignore speeds in that counting?
 
  • #4
IMO, if you are doing the compression with high velocity compared with the mean velocity of the particles in the gas and by small steps, it seems one can well defend this procedure.

Best wishes

DaTario
 
  • #5
naima said:
Hi all,

Entropy uses the 6N dimensional phase space. But ...
Roger Balian in "Scientific American" takes one liter gas in a cube and he writes:
I can replace the continuous volume by Q = 10^100 sites after having
evacuated the speeds (he says this is possible with quantum mechanics)
He then counts the number of possible places for the N molecules and get the entropy.

How can he do that?

Is the article you're referring to available online? There is a general principle in statistical mechanics that you can get the number of quantum states in a given energy range by calculating the classical phase space volume and dividing by h^M, where h is Planck's constant, M is the number of degrees of freedom (3N for N atoms in a monatomic gas); perhaps that's what he's talking about?
 

1. What is entropy?

Entropy is a measure of the disorder or randomness of a system. It is commonly used in physics and information theory to describe the amount of uncertainty or unpredictability in a system.

2. How is entropy calculated?

The entropy of a system is calculated by multiplying the number of possible configurations of the system by the logarithm of the probability of each configuration. This takes into account both the number of possible states and the likelihood of each state occurring.

3. What is the relationship between entropy and the number of configurations?

The higher the number of configurations a system has, the higher its entropy will be. This means that a more complex or disordered system will have a higher entropy than a simpler or more ordered system.

4. Why is counting the number of configurations important?

Counting the number of configurations is important because it allows us to calculate the entropy of a system, which is a fundamental concept in many scientific fields. It also helps us understand the complexity and behavior of a system.

5. Can entropy be decreased?

No, entropy can only increase or remain constant in a closed system. This is known as the Second Law of Thermodynamics. However, some systems can appear to decrease in entropy if they are able to transfer their disorder to another system, such as living organisms using energy to maintain order within their cells.

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