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I'm not sure if it has been proven mathematically. The statement that the long-term evolution of the system will tend towards equipartition is equivalent to th

I'm not sure if it has been proven mathematically. The statement that the long-term evolution of the system will tend towards equipartition is equivalent to the system being ergodic. Ergodicity means that statistically any particular state is as likely as any other. These systems are observed (both in reality and in simulation) to be consistent with being ergodic. But I'm not sure it's been proven. I'm also not sure that it has been proven that gasses are ergodic either, even though experiments are consistent with them being ergodic.

effie 10y ago
> These systems are observed (both in reality and in simulation) to be consistent with being ergodic. How could one possibly conclude that system is ergodic from observation? I thought ergodicity is a property of infinite time averages. Globular clusters do not exist indefinitely in the same macrostate, they lose stars as they evolve.
- antognini 10y ago
  This is not my specialty so I may be getting some details wrong here. I don't mean so much that globular clusters are ergodic as few-body interactions are ergodic. It has at least been proven that three-body interactions are chaotic, which implies that all microstates are accessible to the system. This is a necessary requirement for ergodicity, but I don't believe that it implies that the interactions are necessarily ergodic. All I really know is that in practice globular clusters are observed to obey equipartition of energy, as are the average outcomes of large numbers of few-body interactions.
- hansen 10y ago
  Ergodicity in statistical mechanics roughly means that you can replace an average over time by an average over states. In practice this means that within the time it takes to perform your measurement the system should move through a lot of “typical” states. So for everything that matters: If statistical mechanics works you can conclude that the system is ergodic. And if you observe long-time correlations it’s not.

effie 10y ago

> These systems are observed (both in reality and in simulation) to be consistent with being ergodic. How could one possibly conclude that system is ergodic from observation? I thought ergodicity is a property of infinite time averages. Globular clusters do not exist indefinitely in the same macrostate, they lose stars as they evolve.

antognini 10y ago
This is not my specialty so I may be getting some details wrong here. I don't mean so much that globular clusters are ergodic as few-body interactions are ergodic. It has at least been proven that three-body interactions are chaotic, which implies that all microstates are accessible to the system. This is a necessary requirement for ergodicity, but I don't believe that it implies that the interactions are necessarily ergodic. All I really know is that in practice globular clusters are observed to obey equipartition of energy, as are the average outcomes of large numbers of few-body interactions.
hansen 10y ago
Ergodicity in statistical mechanics roughly means that you can replace an average over time by an average over states. In practice this means that within the time it takes to perform your measurement the system should move through a lot of “typical” states. So for everything that matters: If statistical mechanics works you can conclude that the system is ergodic. And if you observe long-time correlations it’s not.