Intro statistical mechanics question

[Coffee_]

Consider the quote ''The macrostate which corresponds to the highest number of microstates which result in that macrostate, is the state which will be observed.''

Can someone specify in which context this is correct because I'm quite confused by it. If I have an isolated box with N particles in it, clearly it has some definite macrostate. Then the macrostate is definite, and not decided by the highest number of microstates. So I'd like some elaboration on what it means.

 

[marcusl]

What they mean is that each macrostate can be produced by a number W of indistinguishable microstates. The most probable macrostate is the one for which W is the largest. Put differently, the entropy is $S=k_B lnW$ in this case, so the preferred state is the one with highest entropy.

 

[jfizzix]

Consider the quote ''The macrostate which corresponds to the highest number of microstates which result in that macrostate, is the state which will be observed.''

Can someone specify in which context this is correct because I'm quite confused by it. If I have an isolated box with N particles in it, clearly it has some definite macrostate. Then the macrostate is definite, and not decided by the highest number of microstates. So I'd like some elaboration on what it means.

At any given instant, a box containing a gas of N particles has some microstate, defined by the states of all the individual particles making up the gas. It's also true that that configuration of particles defines the macrostate of the gas (i.e., its bulk properties).

At any given instant, the particles making up the gas are randomly colliding with one another, exchanging energy and momentum. The microstate of the gas changes randomly, Since the particular microstate defines what the bulk properties are too, the macrostate changes, however slightly as the microstate changes.

Since there are many microstates that could correspond to the same macrostate, and all microstates are equally likely, we can understand the following. The macrostate that has the most microstates is the one that's most likely to be seen at any given instant. Since there are vastly more microstates where the configurations of particles is nearly evenly distributed, we almost never see, for example, a gale force wind spontaneously blow in a still, sealed room.