content_image/335779.jpg content_image/335781.jpg content_image/335780.jpg content_image/335782.jpg content_image/335783.jpg content_image/335784.jpg content_image/335785.jpg content_image/335786.jpg content_image/335787.jpg content_image/335788.jpg
where ¯ β stands for the average of β over f ( β ): 〈 β 〉 β = ¯ β . The PDF averaged over f ( β ) is given by 

with 

<img src='content_image/335779.jpg'>

<img src='content_image/335781.jpg'>

<img src='content_image/335780.jpg'>

The PDF of harmonic oscillators in the local equilibrium state with a given inverse temperature β is expressed by 

<img src='content_image/335782.jpg'>

The PDF averaged over f ( β ) is given by 

with 

<img src='content_image/335783.jpg'>

<img src='content_image/335784.jpg'>

<img src='content_image/335785.jpg'>

It is easy to see that PDFs given by Eqs. (85) and (89) have the same structure as those given by Eqs. (16) and (29) derived by the MEMs. For example, Eq. (85) for ideal gases may be rewritten as 

<img src='content_image/335786.jpg'>

with 

or equivalently 

<img src='content_image/335787.jpg'>

<img src='content_image/335788.jpg'>

