# Pressure in canonical ensemble

• SchroedingersLion
KmBGlxUXLVY&qid=ZDYHAXxsNQ&oe=UTF-8In summary, pressure in a closed system is the average force of particles hitting against the wall of said system. The obvious way to manipulate pressure in a closed system is to either shrinkf

#### SchroedingersLion

Greetings,

I am having a hard time in understanding intuitively how pressure does not automatically stay constant in a canonical ensemble (=NVT ensemble).

Pressure in a closed system is the average force of particles hitting against the wall of said system. The obvious way to manipulate pressure in a closed system is to either shrink the volume so the particles would have less space and collide with the boundary more often, or to increase the temperature so the average momentum of the particles would increase and thus the force they hit the boundary with.
But both V and T stay constant in the canonical ensemble.

So how come pressure fluctuates?

Regards
SL

A canonical ensemble represents the possible states of a thermodynamic system which is characterized by a fixed number of particles and a fixed volume and which is allowed to exchange heat with a huge heat bath at a "fixed" temperature T. Hence, the energy of such a system can fluctuate when considering its behaviour in course of time.

As you stated, the pressure is an average quantity. The forces with which the particles hit the walls are, at the microscopic level, wildly fluctuating quantities. What you control from outside is the volume, and if the volume and the temperature are held constant, then the average pressure is a constant. There are always fluctuations about the average value, along with the energy, as pointed out by Lord Jestocost above.

Thanks guys.

I was under impression that the three 'constant' quantities, like N,V,T in the canonical ensemble or N,V,E in the microcanonical ensemble can also fluctuate around a constant average (N and V can even be constant all time). For example, when learning about how to simulate a thermostat in a molecular dynamics simulation, it was said that even in a canonical ensemble, T can fluctuate and only the average stays constant.
If it is the same with p, then one could call the N,V,T ensemble also a N,V,T,p ensemble, right?

How would one define a canonical ensemble with changing temperature? What are the conditions?