About Ensemble Average for gas molecules(classical mechanics regime)

[Noh-hoon Lee]

I have some question about Ensemble Average.

The macroscopic variable of fluid is average of microscopic variable of gas molecule.

And if time average is same with spatial average I know as it called edgodic.

My question is that if two different microscopic variables which have same average value, like center of mass, momentum, translational energy, (angular momentum has some error but it is very small so I ignore it.(it is acceptable error))

Does it can be seen as a same state for macroscopic view?

 

[jfizzix]

Every microstate is unique configuration of particle states and. In pursuit of thermodynamics, we say that there are many different microstates for the same macrostate, so long as they have the same ensemble averages. The number of microstates for a given macrostate determines its entropy, and from there, all the rest of thermodynamics can follow.

I have some question about Ensemble Average.

The macroscopic variable of fluid is average of microscopic variable of gas molecule.

And if time average is same with spatial average I know as it called edgodic.

My question is that if two different microscopic variables which have same average value, like center of mass, momentum, translational energy, (angular momentum has some error but it is very small so I ignore it.(it is acceptable error))

Does it can be seen as a same state for macroscopic view?

 

[Noh-hoon Lee]

thank you for your reply :) It's really helpful