Does the Equal A Priori Probabilities Assumption Hold for Interacting Gases?

In summary, the question is whether the equal a priori probabilities assumption holds for an interacting system in the microcanonical ensemble. The answer is yes, as long as the system is in equilibrium and all microstates are equally probable. The hamiltonian must also be conserved due to Noether's theorem and the total energy remains fixed. Defining equilibrium for many interacting particles and exploring the ergodic assumption are areas of interest, with numerous references available online.
  • #1
gonadas91
80
5
Hi! My question has to be with the equal a priori probabilities assumption in the microcanonical ensemble when we consider an interacting system, that is, particles interacting between them but no external work or heat is done over the system. Does this assumption still hold for such a system? Thanks!
 
Physics news on Phys.org
  • #2
Yes. If the system is in equilibrium, all microstates are equally probable, even for an interacting system.
 
  • #3
So, because the interactions don't depend on time, the hamiltonian must be a conserved quantity according to Noether's theorem, and the total energy is conserved or fixed. However, I would like to know more about how to define equilibrium for a system of many interacting particles. Is there any reference to look at this closer? Also, the ergodic assumption is of interest for me, in the case of an interacting system. If you assume the equal a priori probabilities, then for very long times, all states are visited regularly with the same frecuency. Is there any reference too to see how this works? Or any attempts to prove that that hav been made?

Thank you!
 
  • #4
Several references on ergodicity in interacting systems. I just typed those words in google and got may pages.
 

1. What is a classical interacting gas?

A classical interacting gas is a system of particles that interact with each other through classical forces, such as van der Waals forces or Coulombic forces. This type of gas is often found in high temperature and low density conditions, where quantum effects can be ignored.

2. What are the properties of a classical interacting gas?

The properties of a classical interacting gas include the ability to expand and contract, as well as exert pressure and have a definite volume. The particles in the gas also have a distribution of velocities and can collide with each other.

3. How is the behavior of a classical interacting gas described?

The behavior of a classical interacting gas can be described using statistical mechanics, specifically the Maxwell-Boltzmann distribution. This distribution describes the probability of a particle having a certain velocity in the gas.

4. What is the difference between a classical and quantum gas?

A classical gas is described by classical mechanics and can be thought of as a collection of point particles that interact with each other. A quantum gas, on the other hand, takes into account the wave nature of particles and requires a quantum mechanical description. Additionally, a quantum gas can exhibit different properties, such as Bose-Einstein condensation.

5. What are some real-world examples of classical interacting gases?

Some real-world examples of classical interacting gases include air, which is a mixture of gases that interact with each other through classical forces, and steam, which consists of water molecules that interact with each other through van der Waals forces.

Similar threads

Replies
4
Views
1K
Replies
8
Views
1K
  • Classical Physics
Replies
9
Views
1K
Replies
18
Views
1K
Replies
5
Views
575
Replies
2
Views
868
  • Classical Physics
Replies
10
Views
1K
  • Classical Physics
Replies
3
Views
1K
  • Materials and Chemical Engineering
Replies
1
Views
440
  • Classical Physics
Replies
6
Views
820
Back
Top