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## Main Question or Discussion Point

A system is in contact with a reservoir at a specific temperature. The macrostate of the system is specified by the triple (N,V,T) viz., particle number, volume and temperature.

The canonical ensemble can be used to analyze the situation. In the canonical ensemble, the system can exchange energy with the reservoir, with the system energy varying, in principle, from zero to infinity.

I don't understand how the system energy can vary once we specify (N,V,T). The internal energy, after all, can be considered to be a function of T and V, U=U(T,V).

Surely, we're not talking about the fluctuation, i.e. the standard deviation in energy, since that is very small for systems with large N. Where am I going wrong?

The canonical ensemble can be used to analyze the situation. In the canonical ensemble, the system can exchange energy with the reservoir, with the system energy varying, in principle, from zero to infinity.

I don't understand how the system energy can vary once we specify (N,V,T). The internal energy, after all, can be considered to be a function of T and V, U=U(T,V).

Surely, we're not talking about the fluctuation, i.e. the standard deviation in energy, since that is very small for systems with large N. Where am I going wrong?