On the entry of Gibb\'s entropy formula on Wikipedia, the following definition i

Question

On the entry of Gibb's entropy formula on Wikipedia, the following definition is given: "The macroscopic state of the system is defined by a distribution on the microstates that are accessible to a system in the course of its thermal fluctuations." (I will assume that this description is correct. If not, this question does not apply.)

I'm having a hard time grasping exactly what this description tries to say. I initially thought that the distribution of microstates was given by which microstates that could instantiate the macrostate in question. However, both "accessible" and "in the course of its thermal fluctuations" makes me wonder about if this interpretation is correct.

When reading the description above, it seems to me that you should start of with a certain microstate that instantiate the macrostate and then see how many states that are accessible, that is, that could be the case within the time course of some time unit defined by the thermal fluctuation...Ehh....I might have lost myself there.

Could somebody deconstruct the description cited above?

Explanation / Answer

The term "accessible" is used in a somewhat sloppy way in the article (used sometimes, sometimes omitted). I think it's to be understood implicitely that microstates are accessible, i.e. they can evolve within a connected set. The macroscopically constrained set is called a statistical ensemble, for example of constant energy (so an example of a non-accessible microstate would be a state with another energy and shouldn't be counted then). This is obvious if the microstates are generated incrementally from each other but not obvious if you're generating them by randomizing configurations (see the interesting concept of the ergodic hypothesis).

So your quote says that the macroscopic state is a weighted collection of microstates, and that they have to be physically realizable from your starting conditions. The stuff about "thermal fluctuations" means you can't have for example a magic force you can enable at a point in time which pulls all the atoms of a gas into the corner of the room - I guess another way of putting it is that the walk through the configuration space of the system has to be a random walk.

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