BELIEVE   ME   NOT!    - -     A   SKEPTIC's   GUIDE  

The Most Probable

So what? Well, here's the thing: we know that all accessible states of the system are a priori equally likely; however, the number  $\Omega$  of accessible states will depend upon the division of the total energy  U  between  U₁  and  U₂. Moreover, for a certain value of  U₁  (and therefore of   U₂ = U - U₁),  $\Omega$  will be a maximum - i.e. that value of  U₁  will make possible the largest variety of equally likely random states of the system and consequently we will be more likely, on average, to find the system in states with that value of  U₁  than in other states^15.12 with different values of  U₁.

This special value of  U₁  is called (reasonably enough) the "most probable value" and is given the symbolic representation  $\hat{U}_1$.