Reference systems and umbrella sampling

We have several times above exploited knowledge of a physically relevant reference system to write 

In this approach is selected on the basis of physical insight, and the goal 

Another view is that the additional factor e serves to broaden the sampling. With this view, we might consider another configurational function fl(W + 1) that helpfully broadens the sampling and write 

Intuitively, this corresponds to the possibilities that the distinguished molecule is present or not. Show that 

3 Comparisons available from statistical data allow us to discuss a foundational issue, the possibility of entropy calculated from the trajectory of motion, raised years ago (Ma, 1985). This is a digression that illustrates the use of reference systems and statistical comparisons for the conceptuahzation of entropy. 

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