The likelihood that all the smoke particles in a smoke-filled room will move as a result of their chaotic motions into one corner of the room is analogous to the likelihood that nearly all the coins in a set of 10 23 tosses will land on heads. A ' random motion model' for molecules is much more useful than a model that tries to calculate the motion of every molecule. There are many different ways for the molecules to move, and the details of why they move in one way or another is very sensitive to exactly where they are and how they are moving - and is very much out of our control. In many ways, molecules in physics are like multi-sided dice, and the likelihood that a particle will be located in a particular location in space (or have a particular energy) is analogous to the likelihood that a multi-sided die will land on a particular side. What does a discussion about probabilities have to do with a physical law? Physical laws are always true, aren't they? And isn't probability really about things that are only sometimes true?

In order to codify and elaborate our understanding of these results, we turn to the ideas of probability to understand how energy tends to be distributed. But there are a lot of thermal things that don't happen that are perfectly consistent with the 1st law like thermal energy flowing from a cold object to a hotter object. In our lead-in discussion to why we need a 2nd law, we point out that energy conservation - the 1st law of thermodynamics - suffices to rule out a lot of thermal sort of things that don't happen - like things getting warmer without any source of warmth.

Law of entropy