# What does zero partition function physically mean?

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 P: 109 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?
 P: 5,462 The partition function is defined by an exponential. Can an exponential be zero?
P: 109
 Quote by Studiot 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.

 P: 5,462 What does zero partition function physically mean? And when do these delightful occurrences happen?
P: 109
 Quote by Studiot And when do these delightful occurrences happen?
What do you mean?
 P: 901 It means the system is impossible. There are no valid states, so it is unrealizable.
P: 5,462
 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.
 P: 109 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?
 P: 5,462 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.

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