Why Is Entropy Non-Zero in This Hamiltonian System?

In summary, the conversation discusses how to calculate the value of S, with a particular focus on the Ising chain. It is suggested to use the exact solution for the partition function Z in order to determine S, and in other situations the number of states corresponding to T and H may also be used.
  • #1
romeo31415
5
0

Homework Statement


Bonjour,

Given the hamiltonian

image.png

Show that
image.png

The Attempt at a Solution


image.png
[/B]

https://mail.google.com/mail/u/0/?ui=2&ik=926d313718&view=fimg&th=14b1676f1c775525&attid=0.4&disp=emb&realattid=ii_14b16759c66f2c07&attbid=ANGjdJ8nHkVansCbZY79hWetamch9gX2IeJFX1IdCsZvvCq0wrrFx61OU_3uTU3s5BodY--fZWORr1KruMhwcc1mUUynX4vyaIqg7Pee2njVuAEpG5rRFC7jNJ4cxBE&sz=w874-h108&ats=1422015353399&rm=14b1676f1c775525&zw&atsh=1

I cannot explain why S=0
 

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  • #2
One thing you may be able do for is use the exact solution for the partition function ##Z## of the Ising chain.
##S = \partial_T k_B T \ln Z##

In other situations like this one may be able to start by using ##S = k_B \ln \Omega(T, H) ##, where ##\Omega(T, H) ## is the number of states corresponding to T and H.
 
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FAQ: Why Is Entropy Non-Zero in This Hamiltonian System?

1. What is entropy and why is it important?

Entropy is a measure of the disorder or randomness in a system. It is important because it helps us understand the direction of spontaneous processes and the efficiency of energy conversion.

2. How is entropy related to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system tends to increase over time. This means that in any natural process, the total disorder or randomness of the system will increase, leading to a decrease in usable energy.

3. Why is entropy always increasing?

Entropy is always increasing because of the random nature of energy transfer and the tendency for systems to move towards a state of maximum disorder. This is in accordance with the second law of thermodynamics.

4. What factors affect the entropy of a system?

The entropy of a system is affected by the number of particles present, the size of the system, and the temperature. Generally, as the number of particles and the size of the system increase, so does the entropy. However, as temperature increases, the entropy decreases.

5. Can entropy ever be reduced or reversed?

In a closed system, entropy will always tend to increase. However, in an open system, where there is an input of energy or matter, it is possible for entropy to decrease or be reversed. This is because the input of energy or matter can decrease the overall disorder of the system.

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