What does zero partition function physically mean?

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?

Studiot

The partition function is defined by an exponential.

Can an exponential be zero?

cryptist

Yes. Since Ʃ e^-βE_s is zero when T (temperature) goes to zero, or E_s goes to infinity.

Studiot

And when do these delightful occurrences happen?

cryptist

What do you mean?

Khashishi

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

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"

and you will have worked out your answer.

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

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?

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.