# Probability and statistical mechanics

## Main Question or Discussion Point

(I didn't know where to put this one, so somebody will eventually move it, I predict...)

This is a absolute newbie-question, so don't be evil!

Why does statistical mechanics deal with probabilities?
ASAIK, statistical mechanics is built on classical mechanics, where it is possible to predict the infinite future, if all the parameters of a system is known.

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## Answers and Replies

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It uses probabilities because it would be a major headache otherwise.

Imagine a container full of air particles. There is a ton of different arrangements possible, and the arrangements are always changing. Therefore it's easy to look at it in terms of the most probable "state" instead of trying to analyze each one individually.

And then there is also quantum mechanics where it seems impossible to observe an event without affecting it, so we can only deal with probabilities as well.

I guess the short answer is that at the atomic level, so many different things are possible, that it is practically impossible to predict EXACTLY what will happen. This is why we use probabilities.

Galileo
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Why does statistical mechanics deal with probabilities?
ASAIK, statistical mechanics is built on classical mechanics, where it is possible to predict the infinite future, if all the parameters of a system is known.
Your last line conveys the key difficulty.
For systems with a large (read humongous) number of degrees of freedom it is practically impossible to determine the initial state. Take a mole of atoms in a container (like an ideal gas). To determine the initial condition you need the simultaneous measurement of N_A (Avogadro's number) positions and momenta. It is practically without meaning. Probability allows the only hope for predictions.

To add on, let's consider what would happen if we somehow knew all the trajectories for all time. What does this tell us? Okay, we know "everything" about the system, but that's a ridiculous amount of information to make sense of. Really, the averages are a very good representation of the behavior of the system (read Landau & Lif****z for a proof that the standard deviation for such a system goes like $$1/\sqrt{N}$$), but it's one or a few numbers rather than $$6 N$$ functions of time. Which one would you rather deal with?

Edit: Are you serious? This thing blanks out Lifsitz' name?