What does zero partition function physically mean?

In summary, the partition function being zero in thermodynamics results in the free energy becoming infinity and the entropy becoming negative. This means that the system is impossible and cannot exist in any valid states. This can happen when the temperature approaches absolute zero or the energy levels approach infinity. If the partition function is close to zero, the free energy will be extremely large, but there is no physical process that can result in this scenario. It is a hypothetical question that has no real consequences.
  • #1
cryptist
121
1
Is there a physical process in thermodynamics that results the value of the partition function as zero?

When partition function is zero, then free energy becomes infinity, and it also yields negative entropy (at least within the system). Are there physical meanings of these?
 
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  • #2
The partition function is defined by an exponential.

Can an exponential be zero?
 
  • #3
Studiot said:
The partition function is defined by an exponential.

Can an exponential be zero?

Yes. Since Ʃ e-βEs is zero when T (temperature) goes to zero, or Es goes to infinity.
 
  • #4
And when do these delightful occurrences happen?
 
  • #5
Studiot said:
And when do these delightful occurrences happen?

What do you mean?
 
  • #6
It means the system is impossible. There are no valid states, so it is unrealizable.
 
  • #7
What do you mean?

You asked what a zero partition function means.

You were so nearly there I'm sure you would rather work it out for yourself than just be told. It's not a question you would ask if you were not interested so I was trying to hint.

So I am basically saying look at the definition or formula for the partition function and ask

"under what conditions? ie under what values of the variables? can this equal zero"

and you will have worked out your answer.

Please note that your β = 1/kT so if T = 0 you are dividing by zero.
 
  • #8
Ok. I am just wondering, so, let's say that partition function is not zero but, close to zero. Then, free energy will be very very large. Is there a similar physical process of that? Or what does physically mean?

If there is no physical process like this, consider this as a hypothetical question. What would be the consequences?
 
  • #9
Bear in mind that the phrase 'close to zero' can be misleading.

The scale you refer to is like the temperature scale and the law of diminishing returns - non linear.

The closer you get the harder it become to achieve the next small increment.
 

1. What is the partition function and why is it important in physics?

The partition function is a mathematical function that is used to describe the statistical mechanics of a system. It is important in physics because it allows us to calculate the thermodynamic properties of a system, such as its energy, temperature, and entropy.

2. How is the partition function related to the probability of a system being in a particular state?

The partition function is related to the probability of a system being in a particular state through the Boltzmann distribution. This states that the probability of a system being in a particular state is proportional to the exponential of the energy of that state divided by the temperature of the system.

3. What happens when the partition function is equal to zero?

When the partition function is equal to zero, it means that there are no accessible energy levels for the system. This could happen if the system has a very low temperature or if there are constraints on the energy levels of the system.

4. Can a system have a negative partition function?

No, a system cannot have a negative partition function. The partition function is a mathematical function and, by definition, it cannot have a negative value. A negative partition function would imply that the system has a negative temperature, which is not physically meaningful.

5. How does the partition function change with temperature?

The partition function is directly proportional to the temperature of the system. As the temperature increases, the partition function also increases, indicating that there are more accessible energy levels for the system. Conversely, as the temperature decreases, the partition function decreases, indicating that there are fewer accessible energy levels.

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