Changes

With really large numbers, the probability of any particular outcome is vanishingly small; the only sensible measure is the accumulated probability, or the probability density, measured in a way that doesn't involve individual outcomes.

With really large numbers, the probability of any particular outcome is vanishingly small; the only sensible measure is the accumulated probability, or the probability density, measured in a way that doesn't involve individual outcomes.

When dealing with thermodynamics, we are dealing with the statistical aggregate behavior of macroscopic pieces of matter, so we have to increase the number of items from 10, or 52, to something like Avogadro's number.  So the number of possible situations, instead of being 10⁶ or 10⁶⁶, is something like 10^{Avogadro's number}.  The enormity of such a number makes a huge amount of difference.

When dealing with thermodynamics, we are dealing with the statistical aggregate behavior of macroscopic pieces of matter, so we have to increase the number of items from 10, or 52, to something like [[Avogadro's number]].  So the number of possible situations, instead of being 10⁶ or 10⁶⁶, is something like 10^{Avogadro's number}, that is, 10^10²³.  The enormity of such a number makes a huge amount of difference.

*You can't ask any questions about individual items—air molecules don't have labels like "Jack of Diamonds".  You can only ask questions about the aggregate behavior of macroscopic pieces of space.

*You can't ask any questions about individual items—air molecules don't have labels like "Jack of Diamonds".  You can only ask questions about the aggregate behavior of macroscopic pieces of space.

*While the probabilities of certain outcomes can be mathematically calculated, they are so small that, as a practical matter, we can say that '''they do not occur'''.  People sometimes like to say things like "The second law of thermodynamics means that it is very unlikely that heat will travel from a colder object to a warmer one."  That's a fallacious way of thinking about it.  It just doesn't occur.

*While the probabilities of certain outcomes can be mathematically calculated, they are so small that, as a practical matter, we can say that '''they do not occur'''.  People sometimes like to say things like "The second law of thermodynamics means that it is very unlikely that heat will travel from a colder object to a warmer one."  That's a fallacious way of thinking about it.  It is a [[statistical impossibility]]—it just doesn't occur.

*An example is the question of how likely it is that all the air molecules in a room will move to one corner, asphyxiating everyone.<ref>Actually, conservation of momentum requires that we consider half the molecules going to one corner and the other half to the opposite corner.</ref>  This is sometimes worked out in physics classes.  But the conclusion has to be that this occurrence, or anything remotely resembling it, just doesn't happen.

*An example is the question of how likely it is that all the air molecules in a room will move to one corner, asphyxiating everyone.<ref>Actually, conservation of momentum requires that we consider half the molecules going to one corner and the other half to the opposite corner.</ref>  This is sometimes worked out in physics classes.  But the conclusion has to be that this occurrence, or anything remotely resembling it, might have a probability on the order of 1 in 10^10²³&mdash;it just doesn't happen.

==Application to molecular behavior==

==Application to molecular behavior==