Thermodynamics: The principle of equal (a priori) probabilities

[nhanle]

Homework Statement

The principle of equal a priori probabilities (PEEP) states:

for an isolated system, all microstates compatible with the given constraints are equally likely to occur

Homework Equations

In the case of the Gibbs entropy, for a particular energy U, the entropy is
$$S = -k_{b}\sum_{i} P_{i} lnP_{i}$$
Should the probability for a system that, at any instance, being in a particular configuration is the same as stated in PEEP? Why and why not?

(I myself do not understand the question, this is an essay type question)

The Attempt at a Solution

I have no idea because the principle is a principle, I cannot justify
However for the Gibbs entropy, it is clearly that for different energy U, you cannot have the same probability of microstates ensembles/distribution as the entropy would stay the same.

So, basically, I have no idea how to attempt the question... can anyone help?

 

[L-x]

I *think* the question is asking "should the probability of the system being in a particular configuration be the same as is stated in PEEP" but that doesn't seem right.

Is there a typo in your version of the question? It's very hard to understand what you're being asked for.