# How do I find the temperature fluctuation in a grand canonical ensemble?

I think that when particles and energy are allowed to freely leave the grand ensemble like that, there'll always be fluctuation in temperature despite the heat bath. But I only see particle and energy fluctuations, and temperature seems to always be considered at constant. So how do I find the T fluctuation, and is it necessary? Thanks.

• The temperature doesn't fluctuate in the grand canonical ensemble. Temperature is more like a parameter you put in to specify which ensemble you're working with. – knzhou Oct 17 '16 at 6:09
• But I find in here: link that T is not fixed in a canonical ensemble? Is it different in the GCE? – Kim Dong Oct 17 '16 at 9:26

• Microcanonical ensemble: fixed $N,V,E$
• Canonical ensemble: fixed $N,V,T$
• Grand canonical ensemble: fixed $\mu,V,T$
where $\mu$ is the chemical potential.