Pressure in canonical ensemble

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SUMMARY

The discussion centers on the behavior of pressure in a canonical ensemble (NVT ensemble), where the number of particles (N), volume (V), and temperature (T) are held constant. Despite these constants, pressure fluctuates due to the microscopic nature of particle interactions, which leads to variations in the forces exerted on the walls of the system. The average pressure remains constant, but fluctuations around this average occur, similar to energy and temperature fluctuations in the system. The conversation also touches on the potential for defining a canonical ensemble with varying temperature and the implications of such fluctuations.

PREREQUISITES
  • Understanding of canonical ensemble (NVT ensemble) in statistical mechanics
  • Familiarity with thermodynamic concepts such as pressure, temperature, and volume
  • Knowledge of molecular dynamics simulations and thermostats
  • Basic principles of statistical fluctuations in physical systems
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  • Research the concept of pressure fluctuations in canonical ensembles
  • Study the role of thermostats in molecular dynamics simulations
  • Explore the implications of temperature fluctuations in thermodynamic systems
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Physicists, researchers in statistical mechanics, and students studying thermodynamics who seek to understand the nuances of pressure behavior in canonical ensembles.

SchroedingersLion
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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
 
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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?
 

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