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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 states15.12 with different values of  U1.

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


Jess H. Brewer - Last modified: Mon Nov 16 16:04:42 PST 2015