What does zero partition function physically mean?

1. Dec 9, 2012

cryptist

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?

2. Dec 9, 2012

Studiot

The partition function is defined by an exponential.

Can an exponential be zero?

3. Dec 9, 2012

cryptist

Yes. Since Ʃ e-βEs is zero when T (temperature) goes to zero, or Es goes to infinity.

4. Dec 9, 2012

Studiot

And when do these delightful occurrences happen?

5. Dec 9, 2012

cryptist

What do you mean?

6. Dec 9, 2012

Khashishi

It means the system is impossible. There are no valid states, so it is unrealizable.

7. Dec 9, 2012

Studiot

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"

Please note that your β = 1/kT so if T = 0 you are dividing by zero.

8. Dec 9, 2012

cryptist

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. Dec 9, 2012

Studiot

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.